3x(x+4)(x-13)=0

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Solution for 3x(x+4)(x-13)=0 equation: 


Simplifying
3x(x + 4)(x + -13) = 0

Reorder the terms:
3x(4 + x)(x + -13) = 0

Reorder the terms:
3x(4 + x)(-13 + x) = 0

Multiply (4 + x) * (-13 + x)
3x(4(-13 + x) + x(-13 + x)) = 0
3x((-13 * 4 + x * 4) + x(-13 + x)) = 0
3x((-52 + 4x) + x(-13 + x)) = 0
3x(-52 + 4x + (-13 * x + x * x)) = 0
3x(-52 + 4x + (-13x + x2)) = 0

Combine like terms: 4x + -13x = -9x
3x(-52 + -9x + x2) = 0
(-52 * 3x + -9x * 3x + x2 * 3x) = 0
(-156x + -27x2 + 3x3) = 0

Solving
-156x + -27x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-52 + -9x + x2) = 0

Factor a trinomial.
3x((-4 + -1x)(13 + -1x)) = 0

Ignore the factor 3.

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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 3
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {0, -4, 13}

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