2(y^2-15)=-7y

Solution for 2(y^2-15)=-7y equation:

Simplifying
2(y2 + -15) = -7y

Reorder the terms:
2(-15 + y2) = -7y
(-15 * 2 + y2 * 2) = -7y
(-30 + 2y2) = -7y

Solving
-30 + 2y2 = -7y

Solving for variable 'y'.

Reorder the terms:
-30 + 7y + 2y2 = -7y + 7y

Combine like terms: -7y + 7y = 0
-30 + 7y + 2y2 = 0

Factor a trinomial.
(-6 + -1y)(5 + -2y) = 0

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

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 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 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-6, 2.5}