2x^3+24x^2=136x-2x^2

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Solution for 2x^3+24x^2=136x-2x^2 equation: 


Simplifying
2x3 + 24x2 = 136x + -2x2

Reorder the terms:
24x2 + 2x3 = 136x + -2x2

Solving
24x2 + 2x3 = 136x + -2x2

Solving for variable 'x'.

Reorder the terms:
-136x + 24x2 + 2x2 + 2x3 = 136x + -2x2 + -136x + 2x2

Combine like terms: 24x2 + 2x2 = 26x2
-136x + 26x2 + 2x3 = 136x + -2x2 + -136x + 2x2

Reorder the terms:
-136x + 26x2 + 2x3 = 136x + -136x + -2x2 + 2x2

Combine like terms: 136x + -136x = 0
-136x + 26x2 + 2x3 = 0 + -2x2 + 2x2
-136x + 26x2 + 2x3 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-136x + 26x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-68 + 13x + x2) = 0

Factor a trinomial.
2x((-17 + -1x)(4 + -1x)) = 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 '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -17, 4}

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