0=x^3+x^2-42x

Solution for 0=x^3+x^2-42x equation:

Simplifying
0 = x3 + x2 + -42x

Reorder the terms:
0 = -42x + x2 + x3

Solving
0 = -42x + x2 + x3

Solving for variable 'x'.
Remove the zero:
42x + -1x2 + -1x3 = -42x + x2 + x3 + 42x + -1x2 + -1x3

Reorder the terms:
42x + -1x2 + -1x3 = -42x + 42x + x2 + -1x2 + x3 + -1x3

Combine like terms: -42x + 42x = 0
42x + -1x2 + -1x3 = 0 + x2 + -1x2 + x3 + -1x3
42x + -1x2 + -1x3 = x2 + -1x2 + x3 + -1x3

Combine like terms: x2 + -1x2 = 0
42x + -1x2 + -1x3 = 0 + x3 + -1x3
42x + -1x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
42x + -1x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(42 + -1x + -1x2) = 0

Factor a trinomial.
x((6 + -1x)(7 + 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 3
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
Solution
x = {0, 6, -7}