(y-2)(y+5)=

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

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

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

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

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

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

Solving
-10 + 3y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-5, 2}