13x^2-x^3+x=x^2+36x

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Solution for 13x^2-x^3+x=x^2+36x equation: 


Simplifying
13x2 + -1x3 + x = x2 + 36x

Reorder the terms:
x + 13x2 + -1x3 = x2 + 36x

Reorder the terms:
x + 13x2 + -1x3 = 36x + x2

Solving
x + 13x2 + -1x3 = 36x + x2

Solving for variable 'x'.

Reorder the terms:
x + -36x + 13x2 + -1x2 + -1x3 = 36x + x2 + -36x + -1x2

Combine like terms: x + -36x = -35x
-35x + 13x2 + -1x2 + -1x3 = 36x + x2 + -36x + -1x2

Combine like terms: 13x2 + -1x2 = 12x2
-35x + 12x2 + -1x3 = 36x + x2 + -36x + -1x2

Reorder the terms:
-35x + 12x2 + -1x3 = 36x + -36x + x2 + -1x2

Combine like terms: 36x + -36x = 0
-35x + 12x2 + -1x3 = 0 + x2 + -1x2
-35x + 12x2 + -1x3 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35x + 12x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + 12x + -1x2) = 0

Factor a trinomial.
x((-7 + x)(5 + -1x)) = 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 '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 7, 5}

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