24x=2x^2-128

Solution for 24x=2x^2-128 equation:

Simplifying
24x = 2x2 + -128

Reorder the terms:
24x = -128 + 2x2

Solving
24x = -128 + 2x2

Solving for variable 'x'.

Reorder the terms:
128 + 24x + -2x2 = -128 + 2x2 + 128 + -2x2

Reorder the terms:
128 + 24x + -2x2 = -128 + 128 + 2x2 + -2x2

Combine like terms: -128 + 128 = 0
128 + 24x + -2x2 = 0 + 2x2 + -2x2
128 + 24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
128 + 24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(64 + 12x + -1x2) = 0

Factor a trinomial.
2((16 + -1x)(4 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {16, -4}