24x-72=2x^2

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

Simplifying
24x + -72 = 2x2

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

Solving
-72 + 24x = 2x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 12x + -1x2) = 0

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

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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

Combine like terms: 0 + 6 = 6
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}