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

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


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

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

Remove parenthesis around (-4 + 3x)
-4 + 3x + -2x(3x + -4) = 0

Reorder the terms:
-4 + 3x + -2x(-4 + 3x) = 0
-4 + 3x + (-4 * -2x + 3x * -2x) = 0
-4 + 3x + (8x + -6x2) = 0

Combine like terms: 3x + 8x = 11x
-4 + 11x + -6x2 = 0

Solving
-4 + 11x + -6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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
Solution
x = {1.333333333, 0.5}

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