2y^2-15=-7y

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

Simplifying
2y2 + -15 = -7y

Reorder the terms:
-15 + 2y2 = -7y

Solving
-15 + 2y2 = -7y

Solving for variable 'y'.

Reorder the terms:
-15 + 7y + 2y2 = -7y + 7y

Combine like terms: -7y + 7y = 0
-15 + 7y + 2y2 = 0

Factor a trinomial.
(-5 + -1y)(3 + -2y) = 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 '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-5, 1.5}