2X^3+8X^2-42X=0

Solution for 2X^3+8X^2-42X=0 equation:

Simplifying
2X3 + 8X2 + -42X = 0

Reorder the terms:
-42X + 8X2 + 2X3 = 0

Solving
-42X + 8X2 + 2X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2X'.
2X(-21 + 4X + X2) = 0

Factor a trinomial.
2X((-7 + -1X)(3 + -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 '(-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 '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Solution
X = {0, -7, 3}