(3x^2-4x)(6x+3)=0

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Solution for (3x^2-4x)(6x+3)=0 equation: 


Simplifying
(3x2 + -4x)(6x + 3) = 0

Reorder the terms:
(-4x + 3x2)(6x + 3) = 0

Reorder the terms:
(-4x + 3x2)(3 + 6x) = 0

Multiply (-4x + 3x2) * (3 + 6x)
(-4x * (3 + 6x) + 3x2 * (3 + 6x)) = 0
((3 * -4x + 6x * -4x) + 3x2 * (3 + 6x)) = 0
((-12x + -24x2) + 3x2 * (3 + 6x)) = 0
(-12x + -24x2 + (3 * 3x2 + 6x * 3x2)) = 0
(-12x + -24x2 + (9x2 + 18x3)) = 0

Combine like terms: -24x2 + 9x2 = -15x2
(-12x + -15x2 + 18x3) = 0

Solving
-12x + -15x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + -5x + 6x2) = 0

Factor a trinomial.
3x((-1 + -2x)(4 + -3x)) = 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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
4 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -0.5, 1.333333333}

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