2y(y+5)-y(y-2)=-36

Solution for 2y(y+5)-y(y-2)=-36 equation:

Simplifying
2y(y + 5) + -1y(y + -2) = -36

Reorder the terms:
2y(5 + y) + -1y(y + -2) = -36
(5 * 2y + y * 2y) + -1y(y + -2) = -36
(10y + 2y2) + -1y(y + -2) = -36

Reorder the terms:
10y + 2y2 + -1y(-2 + y) = -36
10y + 2y2 + (-2 * -1y + y * -1y) = -36
10y + 2y2 + (2y + -1y2) = -36

Reorder the terms:
10y + 2y + 2y2 + -1y2 = -36

Combine like terms: 10y + 2y = 12y
12y + 2y2 + -1y2 = -36

Combine like terms: 2y2 + -1y2 = 1y2
12y + 1y2 = -36

Solving
12y + 1y2 = -36

Solving for variable 'y'.

Reorder the terms:
36 + 12y + 1y2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 12y + 1y2 = 0

Factor a trinomial.
(6 + y)(6 + y) = 0

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {-6, -6}