Need help with polynomial equations?

I'm having problems with these questions. It's mainly dealing with the principle of zero products and word problems. I've tried drawing a picture and it still doesn't help. Here they are. Thank you.



7x(4x - 5) = 0



-8y^3 - 10y^2 - 3y = 0



Landscaping. A rectangular lawn measures 60 ft by 80 ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?



Tent design. The triangular entrance to a tent is 2 ft taller than it is wide. The area of the entrance is 12 ft^2. Find the height and the base.



Sailing. A triangular sail is 9 m taller than it is wide. The area is 56 m^2. Find the height and the base of the sail.

Need help with polynomial equations?
7x(4x-5)=0



7x=0, 4x-5=0



x=0, x=5/4





-8y3-10y2-3y=0



-y(8y2+10y+3)=0



-y(4y+3)(2y+1)=0



y=0, y=-3/4, y=-1/2
Reply:7x(4x-5) =0

7x = 0

x =0



4x-5 = 0

4x = 5

x=5/4



-8y^3 -10y^2 -3y =0

-y(8y^2+10y+3) =0

-y(4y + 3)(2y+1) =0

-y =0

y =0



4y+3 = 0

4y =-3

y = -3/4

2y + 1 = 0

2y = -1

y = -1/2





First of all the original area is 60 (80) or 4800 sq. ft. Since the new area is half the original area it is 2400 sq. ft.



x is the amount taken out for the sidewalk and it is taken out of each side of the length and the width so

60 -2x is the new width

80-2x is the new length



The area of the new garden is

(60-2x)(80-2x) = 2400

4800 - 120x - 160x +4x^2 = 2400

4x^2 -280x + 4800 = 2400

4x^2 -280x +2400 =0

Divide by 4

x^2 -70x + 600 = 0

Factor

(x-60)(x-10) = 0

x-10 = 0

x =10

x-60 = 0

x= 60

The answer is 10 ft., since the answer of 60 cannot work because if you subtracted 60 you would not have a side since one of the original sides is equal to 60.



Area of a triangle = 1/2bh

x = base

x+2 = height

1/2x(x+2) = 12

Multiply by 2 to get rid of the fraction

x(x+2) = 24

x^2 + 2x = 24

x^2 + 2x -24 =0

(x+6)(x-4) = 0

x+6 = 0

x = -6

x-4 = 0

x = 4

Measures cannot be negative so the base is 4 and the height is 4+2 or 6



Same as the previous problem

A = 1/2bh

x = base

x+9 = height

1/2x(x+9) = 56

mult by 2

x^2 + 9x = 112

x^2 + 9x -112 =0

(x -7)(x + 16) =0

x = 7 or - 16

Cannot be negative

so the base is 7 and the height is 7 + 9 or 16

natural deodorants