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

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


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

Reorder the terms:
(-1 + 3x) * x(4x + 3) = 0

Reorder the terms:
(-1 + 3x) * x(3 + 4x) = 0

Reorder the terms for easier multiplication:
x(-1 + 3x)(3 + 4x) = 0

Multiply (-1 + 3x) * (3 + 4x)
x(-1(3 + 4x) + 3x * (3 + 4x)) = 0
x((3 * -1 + 4x * -1) + 3x * (3 + 4x)) = 0
x((-3 + -4x) + 3x * (3 + 4x)) = 0
x(-3 + -4x + (3 * 3x + 4x * 3x)) = 0
x(-3 + -4x + (9x + 12x2)) = 0

Combine like terms: -4x + 9x = 5x
x(-3 + 5x + 12x2) = 0
(-3 * x + 5x * x + 12x2 * x) = 0
(-3x + 5x2 + 12x3) = 0

Solving
-3x + 5x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 5x + 12x2) = 0

Factor a trinomial.
x((-3 + -4x)(1 + -3x)) = 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 '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.75, 0.3333333333}

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