4y^2-24y=-20

Solution for 4y^2-24y=-20 equation:

Simplifying
4y2 + -24y = -20

Reorder the terms:
-24y + 4y2 = -20

Solving
-24y + 4y2 = -20

Solving for variable 'y'.

Reorder the terms:
20 + -24y + 4y2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -24y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -6y + y2) = 0

Factor a trinomial.
4((1 + -1y)(5 + -1y)) = 0

Ignore the factor 4.
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}