25y^2=50y+75

Solution for 25y^2=50y+75 equation:

Simplifying
25y2 = 50y + 75

Reorder the terms:
25y2 = 75 + 50y

Solving
25y2 = 75 + 50y

Solving for variable 'y'.

Reorder the terms:
-75 + -50y + 25y2 = 75 + 50y + -75 + -50y

Reorder the terms:
-75 + -50y + 25y2 = 75 + -75 + 50y + -50y

Combine like terms: 75 + -75 = 0
-75 + -50y + 25y2 = 0 + 50y + -50y
-75 + -50y + 25y2 = 50y + -50y

Combine like terms: 50y + -50y = 0
-75 + -50y + 25y2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-3 + -2y + y2) = 0

Factor a trinomial.
25((-1 + -1y)(3 + -1y)) = 0

Ignore the factor 25.
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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1, 3}