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

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


Simplifying
3x2(x + 3) + -12x3 = 12x2

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

Combine like terms: 3x3 + -12x3 = -9x3
9x2 + -9x3 = 12x2

Solving
9x2 + -9x3 = 12x2

Solving for variable 'x'.

Reorder the terms:
9x2 + -12x2 + -9x3 = 12x2 + -12x2

Combine like terms: 9x2 + -12x2 = -3x2
-3x2 + -9x3 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-3x2 + -9x3 = 0

Factor out the Greatest Common Factor (GCF), '-3x2'.
-3x2(1 + 3x) = 0

Ignore the factor -3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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
Solution
x = {0, -0.3333333333}

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