0=x^3-6x^2-7x

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Solution for 0=x^3-6x^2-7x equation: 


Simplifying
0 = x3 + -6x2 + -7x

Reorder the terms:
0 = -7x + -6x2 + x3

Solving
0 = -7x + -6x2 + x3

Solving for variable 'x'.
Remove the zero:
7x + 6x2 + -1x3 = -7x + -6x2 + x3 + 7x + 6x2 + -1x3

Reorder the terms:
7x + 6x2 + -1x3 = -7x + 7x + -6x2 + 6x2 + x3 + -1x3

Combine like terms: -7x + 7x = 0
7x + 6x2 + -1x3 = 0 + -6x2 + 6x2 + x3 + -1x3
7x + 6x2 + -1x3 = -6x2 + 6x2 + x3 + -1x3

Combine like terms: -6x2 + 6x2 = 0
7x + 6x2 + -1x3 = 0 + x3 + -1x3
7x + 6x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
7x + 6x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 6x + -1x2) = 0

Factor a trinomial.
x((7 + -1x)(1 + x)) = 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 + -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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, 7, -1}

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