x^3-12x+10=10-3x

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Solution for x^3-12x+10=10-3x equation: 


Simplifying
x3 + -12x + 10 = 10 + -3x

Reorder the terms:
10 + -12x + x3 = 10 + -3x

Add '-10' to each side of the equation.
10 + -12x + -10 + x3 = 10 + -10 + -3x

Reorder the terms:
10 + -10 + -12x + x3 = 10 + -10 + -3x

Combine like terms: 10 + -10 = 0
0 + -12x + x3 = 10 + -10 + -3x
-12x + x3 = 10 + -10 + -3x

Combine like terms: 10 + -10 = 0
-12x + x3 = 0 + -3x
-12x + x3 = -3x

Solving
-12x + x3 = -3x

Solving for variable 'x'.

Reorder the terms:
-12x + 3x + x3 = -3x + 3x

Combine like terms: -12x + 3x = -9x
-9x + x3 = -3x + 3x

Combine like terms: -3x + 3x = 0
-9x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + x2) = 0

Factor a difference between two squares.
x((3 + x)(-3 + x)) = 0


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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 3
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}

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