2x^2=22x-60

Solution for 2x^2=22x-60 equation:

Simplifying
2x2 = 22x + -60

Reorder the terms:
2x2 = -60 + 22x

Solving
2x2 = -60 + 22x

Solving for variable 'x'.

Reorder the terms:
60 + -22x + 2x2 = -60 + 22x + 60 + -22x

Reorder the terms:
60 + -22x + 2x2 = -60 + 60 + 22x + -22x

Combine like terms: -60 + 60 = 0
60 + -22x + 2x2 = 0 + 22x + -22x
60 + -22x + 2x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
60 + -22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11x + x2) = 0

Factor a trinomial.
2((5 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {5, 6}