0=x^3-15x^2+56x

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Solution for 0=x^3-15x^2+56x equation: 


Simplifying
0 = x3 + -15x2 + 56x

Reorder the terms:
0 = 56x + -15x2 + x3

Solving
0 = 56x + -15x2 + x3

Solving for variable 'x'.
Remove the zero:
-56x + 15x2 + -1x3 = 56x + -15x2 + x3 + -56x + 15x2 + -1x3

Reorder the terms:
-56x + 15x2 + -1x3 = 56x + -56x + -15x2 + 15x2 + x3 + -1x3

Combine like terms: 56x + -56x = 0
-56x + 15x2 + -1x3 = 0 + -15x2 + 15x2 + x3 + -1x3
-56x + 15x2 + -1x3 = -15x2 + 15x2 + x3 + -1x3

Combine like terms: -15x2 + 15x2 = 0
-56x + 15x2 + -1x3 = 0 + x3 + -1x3
-56x + 15x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-56x + 15x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-56 + 15x + -1x2) = 0

Factor a trinomial.
x((-8 + x)(7 + -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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 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 + x = 0 + 8

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

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

Simplifying
x = 8

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 8, 7}

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