(y-5)(y+2)=

Solution for (y-5)(y+2)= equation:

Simplifying
(y + -5)(y + 2) = 0

Reorder the terms:
(-5 + y)(y + 2) = 0

Reorder the terms:
(-5 + y)(2 + y) = 0

Multiply (-5 + y) * (2 + y)
(-5(2 + y) + y(2 + y)) = 0
((2 * -5 + y * -5) + y(2 + y)) = 0
((-10 + -5y) + y(2 + y)) = 0
(-10 + -5y + (2 * y + y * y)) = 0
(-10 + -5y + (2y + y2)) = 0

Combine like terms: -5y + 2y = -3y
(-10 + -3y + y2) = 0

Solving
-10 + -3y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(5 + -1y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-2, 5}