2x=12x^3+5x^2

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Solution for 2x=12x^3+5x^2 equation: 


Simplifying
2x = 12x3 + 5x2

Reorder the terms:
2x = 5x2 + 12x3

Solving
2x = 5x2 + 12x3

Solving for variable 'x'.

Reorder the terms:
2x + -5x2 + -12x3 = 5x2 + -5x2 + 12x3 + -12x3

Combine like terms: 5x2 + -5x2 = 0
2x + -5x2 + -12x3 = 0 + 12x3 + -12x3
2x + -5x2 + -12x3 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
2x + -5x2 + -12x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + -5x + -12x2) = 0

Factor a trinomial.
x((1 + -4x)(2 + 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, 0.25, -0.6666666667}

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