(y-7)(5y+8)=0

Solution for (y-7)(5y+8)=0 equation:

Simplifying
(y + -7)(5y + 8) = 0

Reorder the terms:
(-7 + y)(5y + 8) = 0

Reorder the terms:
(-7 + y)(8 + 5y) = 0

Multiply (-7 + y) * (8 + 5y)
(-7(8 + 5y) + y(8 + 5y)) = 0
((8 * -7 + 5y * -7) + y(8 + 5y)) = 0
((-56 + -35y) + y(8 + 5y)) = 0
(-56 + -35y + (8 * y + 5y * y)) = 0
(-56 + -35y + (8y + 5y2)) = 0

Combine like terms: -35y + 8y = -27y
(-56 + -27y + 5y2) = 0

Solving
-56 + -27y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-8 + -5y)(7 + -1y) = 0

Subproblem 1
Set the factor '(-8 + -5y)' equal to zero and attempt to solve:

Simplifying
-8 + -5y = 0

Solving
-8 + -5y = 0

Move all terms containing y to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -5y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5y = 0 + 8
-5y = 0 + 8

Combine like terms: 0 + 8 = 8
-5y = 8

Divide each side by '-5'.
y = -1.6

Simplifying
y = -1.6
Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-1.6, 7}