3x^2-12x-384=4x-5x^2

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Solution for 3x^2-12x-384=4x-5x^2 equation: 


Simplifying
3x2 + -12x + -384 = 4x + -5x2

Reorder the terms:
-384 + -12x + 3x2 = 4x + -5x2

Solving
-384 + -12x + 3x2 = 4x + -5x2

Solving for variable 'x'.

Reorder the terms:
-384 + -12x + -4x + 3x2 + 5x2 = 4x + -5x2 + -4x + 5x2

Combine like terms: -12x + -4x = -16x
-384 + -16x + 3x2 + 5x2 = 4x + -5x2 + -4x + 5x2

Combine like terms: 3x2 + 5x2 = 8x2
-384 + -16x + 8x2 = 4x + -5x2 + -4x + 5x2

Reorder the terms:
-384 + -16x + 8x2 = 4x + -4x + -5x2 + 5x2

Combine like terms: 4x + -4x = 0
-384 + -16x + 8x2 = 0 + -5x2 + 5x2
-384 + -16x + 8x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-384 + -16x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-48 + -2x + x2) = 0

Factor a trinomial.
8((-6 + -1x)(8 + -1x)) = 0

Ignore the factor 8.

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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}

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