-x^3+12x=4x(x^2-7)

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Solution for -x^3+12x=4x(x^2-7) equation: 


Simplifying
-1x3 + 12x = 4x(x2 + -7)

Reorder the terms:
12x + -1x3 = 4x(x2 + -7)

Reorder the terms:
12x + -1x3 = 4x(-7 + x2)
12x + -1x3 = (-7 * 4x + x2 * 4x)
12x + -1x3 = (-28x + 4x3)

Solving
12x + -1x3 = -28x + 4x3

Solving for variable 'x'.

Reorder the terms:
12x + 28x + -1x3 + -4x3 = -28x + 4x3 + 28x + -4x3

Combine like terms: 12x + 28x = 40x
40x + -1x3 + -4x3 = -28x + 4x3 + 28x + -4x3

Combine like terms: -1x3 + -4x3 = -5x3
40x + -5x3 = -28x + 4x3 + 28x + -4x3

Reorder the terms:
40x + -5x3 = -28x + 28x + 4x3 + -4x3

Combine like terms: -28x + 28x = 0
40x + -5x3 = 0 + 4x3 + -4x3
40x + -5x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
40x + -5x3 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(8 + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {0, -2.828427125, 2.828427125}

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