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

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


Simplifying
2(3x + 4) + -4x(3x + 4) = 0

Reorder the terms:
2(4 + 3x) + -4x(3x + 4) = 0
(4 * 2 + 3x * 2) + -4x(3x + 4) = 0
(8 + 6x) + -4x(3x + 4) = 0

Reorder the terms:
8 + 6x + -4x(4 + 3x) = 0
8 + 6x + (4 * -4x + 3x * -4x) = 0
8 + 6x + (-16x + -12x2) = 0

Combine like terms: 6x + -16x = -10x
8 + -10x + -12x2 = 0

Solving
8 + -10x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5x + -6x2) = 0

Factor a trinomial.
2((1 + -2x)(4 + 3x)) = 0

Ignore the factor 2.

Subproblem 1
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 2
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 = {0.5, -1.333333333}

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