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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-2.5, 6}