3x(4+1x)(3-1x)=0

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Solution for 3x(4+1x)(3-1x)=0 equation: 


Simplifying
3x(4 + 1x)(3 + -1x) = 0

Multiply (4 + 1x) * (3 + -1x)
3x(4(3 + -1x) + 1x * (3 + -1x)) = 0
3x((3 * 4 + -1x * 4) + 1x * (3 + -1x)) = 0
3x((12 + -4x) + 1x * (3 + -1x)) = 0
3x(12 + -4x + (3 * 1x + -1x * 1x)) = 0
3x(12 + -4x + (3x + -1x2)) = 0

Combine like terms: -4x + 3x = -1x
3x(12 + -1x + -1x2) = 0
(12 * 3x + -1x * 3x + -1x2 * 3x) = 0
(36x + -3x2 + -3x3) = 0

Solving
36x + -3x2 + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(12 + -1x + -1x2) = 0

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

Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {0, 3, -4}

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