2y^2-24y=-22

Solution for 2y^2-24y=-22 equation:

Simplifying
2y2 + -24y = -22

Reorder the terms:
-24y + 2y2 = -22

Solving
-24y + 2y2 = -22

Solving for variable 'y'.

Reorder the terms:
22 + -24y + 2y2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -24y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -12y + y2) = 0

Factor a trinomial.
2((1 + -1y)(11 + -1y)) = 0

Ignore the factor 2.
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 '(11 + -1y)' equal to zero and attempt to solve:

Simplifying
11 + -1y = 0

Solving
11 + -1y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1y = 0 + -11
-1y = 0 + -11

Combine like terms: 0 + -11 = -11
-1y = -11

Divide each side by '-1'.
y = 11

Simplifying
y = 11
Solution
y = {1, 11}