=X^3-49X

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Solution for =X^3-49X equation: 


Simplifying
0 = X3 + -49X

Reorder the terms:
0 = -49X + X3

Solving
0 = -49X + X3

Solving for variable 'X'.
Remove the zero:
49X + -1X3 = -49X + X3 + 49X + -1X3

Reorder the terms:
49X + -1X3 = -49X + 49X + X3 + -1X3

Combine like terms: -49X + 49X = 0
49X + -1X3 = 0 + X3 + -1X3
49X + -1X3 = X3 + -1X3

Combine like terms: X3 + -1X3 = 0
49X + -1X3 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(49 + -1X2) = 0

Factor a difference between two squares.
X((7 + 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 '(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 '(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, -7, 7}

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