0=3x^4+9x^3-12x^2

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Solution for 0=3x^4+9x^3-12x^2 equation: 


Simplifying
0 = 3x4 + 9x3 + -12x2

Reorder the terms:
0 = -12x2 + 9x3 + 3x4

Solving
0 = -12x2 + 9x3 + 3x4

Solving for variable 'x'.
Remove the zero:
12x2 + -9x3 + -3x4 = -12x2 + 9x3 + 3x4 + 12x2 + -9x3 + -3x4

Reorder the terms:
12x2 + -9x3 + -3x4 = -12x2 + 12x2 + 9x3 + -9x3 + 3x4 + -3x4

Combine like terms: -12x2 + 12x2 = 0
12x2 + -9x3 + -3x4 = 0 + 9x3 + -9x3 + 3x4 + -3x4
12x2 + -9x3 + -3x4 = 9x3 + -9x3 + 3x4 + -3x4

Combine like terms: 9x3 + -9x3 = 0
12x2 + -9x3 + -3x4 = 0 + 3x4 + -3x4
12x2 + -9x3 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
12x2 + -9x3 + -3x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(4 + -3x + -1x2) = 0

Factor a trinomial.
3x2((1 + -1x)(4 + x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 1, -4}

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