9x(x^2+x)=3x(x-2)+5x

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Solution for 9x(x^2+x)=3x(x-2)+5x equation: 


Simplifying
9x(x2 + x) = 3x(x + -2) + 5x

Reorder the terms:
9x(x + x2) = 3x(x + -2) + 5x
(x * 9x + x2 * 9x) = 3x(x + -2) + 5x
(9x2 + 9x3) = 3x(x + -2) + 5x

Reorder the terms:
9x2 + 9x3 = 3x(-2 + x) + 5x
9x2 + 9x3 = (-2 * 3x + x * 3x) + 5x
9x2 + 9x3 = (-6x + 3x2) + 5x

Reorder the terms:
9x2 + 9x3 = -6x + 5x + 3x2

Combine like terms: -6x + 5x = -1x
9x2 + 9x3 = -1x + 3x2

Solving
9x2 + 9x3 = -1x + 3x2

Solving for variable 'x'.

Reorder the terms:
x + 9x2 + -3x2 + 9x3 = -1x + 3x2 + x + -3x2

Combine like terms: 9x2 + -3x2 = 6x2
x + 6x2 + 9x3 = -1x + 3x2 + x + -3x2

Reorder the terms:
x + 6x2 + 9x3 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
x + 6x2 + 9x3 = 0 + 3x2 + -3x2
x + 6x2 + 9x3 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
x + 6x2 + 9x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 6x + 9x2) = 0

Factor a trinomial.
x((1 + 3x)(1 + 3x)) = 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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 3
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0, -0.3333333333, -0.3333333333}

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