24x+216=2x^2

Solution for 24x+216=2x^2 equation:

Simplifying
24x + 216 = 2x2

Reorder the terms:
216 + 24x = 2x2

Solving
216 + 24x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
216 + 24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + 12x + -1x2) = 0

Factor a trinomial.
2((18 + -1x)(6 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Subproblem 2
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
Solution
x = {18, -6}