15y^2=60y+75

Solution for 15y^2=60y+75 equation:

Simplifying
15y2 = 60y + 75

Reorder the terms:
15y2 = 75 + 60y

Solving
15y2 = 75 + 60y

Solving for variable 'y'.

Reorder the terms:
-75 + -60y + 15y2 = 75 + 60y + -75 + -60y

Reorder the terms:
-75 + -60y + 15y2 = 75 + -75 + 60y + -60y

Combine like terms: 75 + -75 = 0
-75 + -60y + 15y2 = 0 + 60y + -60y
-75 + -60y + 15y2 = 60y + -60y

Combine like terms: 60y + -60y = 0
-75 + -60y + 15y2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-5 + -4y + y2) = 0

Factor a trinomial.
15((-1 + -1y)(5 + -1y)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y = 0 + 1

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

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

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

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