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

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


Simplifying
3x2(3x + 4) = 12x(x + 3)

Reorder the terms:
3x2(4 + 3x) = 12x(x + 3)
(4 * 3x2 + 3x * 3x2) = 12x(x + 3)
(12x2 + 9x3) = 12x(x + 3)

Reorder the terms:
12x2 + 9x3 = 12x(3 + x)
12x2 + 9x3 = (3 * 12x + x * 12x)
12x2 + 9x3 = (36x + 12x2)

Add '-12x2' to each side of the equation.
12x2 + -12x2 + 9x3 = 36x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
0 + 9x3 = 36x + 12x2 + -12x2
9x3 = 36x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
9x3 = 36x + 0
9x3 = 36x

Solving
9x3 = 36x

Solving for variable 'x'.

Reorder the terms:
-36x + 9x3 = 36x + -36x

Combine like terms: 36x + -36x = 0
-36x + 9x3 = 0

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-4 + x2) = 0

Factor a difference between two squares.
9x((2 + x)(-2 + x)) = 0

Ignore the factor 9.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, -2, 2}

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