x(x-1)(x+1)=40(3x)

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Solution for x(x-1)(x+1)=40(3x) equation: 


Simplifying
x(x + -1)(x + 1) = 40(3x)

Reorder the terms:
x(-1 + x)(x + 1) = 40(3x)

Reorder the terms:
x(-1 + x)(1 + x) = 40(3x)

Multiply (-1 + x) * (1 + x)
x(-1(1 + x) + x(1 + x)) = 40(3x)
x((1 * -1 + x * -1) + x(1 + x)) = 40(3x)
x((-1 + -1x) + x(1 + x)) = 40(3x)
x(-1 + -1x + (1 * x + x * x)) = 40(3x)
x(-1 + -1x + (1x + x2)) = 40(3x)

Combine like terms: -1x + 1x = 0
x(-1 + 0 + x2) = 40(3x)
x(-1 + x2) = 40(3x)
(-1 * x + x2 * x) = 40(3x)
(-1x + x3) = 40(3x)

Remove parenthesis around (3x)
-1x + x3 = 40 * 3x

Multiply 40 * 3
-1x + x3 = 120x

Solving
-1x + x3 = 120x

Solving for variable 'x'.

Reorder the terms:
-1x + -120x + x3 = 120x + -120x

Combine like terms: -1x + -120x = -121x
-121x + x3 = 120x + -120x

Combine like terms: 120x + -120x = 0
-121x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-121 + x2) = 0

Factor a difference between two squares.
x((11 + x)(-11 + 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 '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

Subproblem 3
Set the factor '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Simplifying
x = 11
Solution
x = {0, -11, 11}

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