12x^3=26x^2+16x

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Solution for 12x^3=26x^2+16x equation: 


Simplifying
12x3 = 26x2 + 16x

Reorder the terms:
12x3 = 16x + 26x2

Solving
12x3 = 16x + 26x2

Solving for variable 'x'.

Reorder the terms:
-16x + -26x2 + 12x3 = 16x + 26x2 + -16x + -26x2

Reorder the terms:
-16x + -26x2 + 12x3 = 16x + -16x + 26x2 + -26x2

Combine like terms: 16x + -16x = 0
-16x + -26x2 + 12x3 = 0 + 26x2 + -26x2
-16x + -26x2 + 12x3 = 26x2 + -26x2

Combine like terms: 26x2 + -26x2 = 0
-16x + -26x2 + 12x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + -13x + 6x2) = 0

Factor a trinomial.
2x((-1 + -2x)(8 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0, -0.5, 2.666666667}

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