2x^2=24x-72

Solution for 2x^2=24x-72 equation:

Simplifying
2x2 = 24x + -72

Reorder the terms:
2x2 = -72 + 24x

Solving
2x2 = -72 + 24x

Solving for variable 'x'.

Reorder the terms:
72 + -24x + 2x2 = -72 + 24x + 72 + -24x

Reorder the terms:
72 + -24x + 2x2 = -72 + 72 + 24x + -24x

Combine like terms: -72 + 72 = 0
72 + -24x + 2x2 = 0 + 24x + -24x
72 + -24x + 2x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
72 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12x + x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {6, 6}