(3x-4)(2x-3)-(3x-4)(6x-1)=

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Solution for (3x-4)(2x-3)-(3x-4)(6x-1)= equation: 


Simplifying
(3x + -4)(2x + -3) + -1(3x + -4)(6x + -1) = 0

Reorder the terms:
(-4 + 3x)(2x + -3) + -1(3x + -4)(6x + -1) = 0

Reorder the terms:
(-4 + 3x)(-3 + 2x) + -1(3x + -4)(6x + -1) = 0

Multiply (-4 + 3x) * (-3 + 2x)
(-4(-3 + 2x) + 3x * (-3 + 2x)) + -1(3x + -4)(6x + -1) = 0
((-3 * -4 + 2x * -4) + 3x * (-3 + 2x)) + -1(3x + -4)(6x + -1) = 0
((12 + -8x) + 3x * (-3 + 2x)) + -1(3x + -4)(6x + -1) = 0
(12 + -8x + (-3 * 3x + 2x * 3x)) + -1(3x + -4)(6x + -1) = 0
(12 + -8x + (-9x + 6x2)) + -1(3x + -4)(6x + -1) = 0

Combine like terms: -8x + -9x = -17x
(12 + -17x + 6x2) + -1(3x + -4)(6x + -1) = 0

Reorder the terms:
12 + -17x + 6x2 + -1(-4 + 3x)(6x + -1) = 0

Reorder the terms:
12 + -17x + 6x2 + -1(-4 + 3x)(-1 + 6x) = 0

Multiply (-4 + 3x) * (-1 + 6x)
12 + -17x + 6x2 + -1(-4(-1 + 6x) + 3x * (-1 + 6x)) = 0
12 + -17x + 6x2 + -1((-1 * -4 + 6x * -4) + 3x * (-1 + 6x)) = 0
12 + -17x + 6x2 + -1((4 + -24x) + 3x * (-1 + 6x)) = 0
12 + -17x + 6x2 + -1(4 + -24x + (-1 * 3x + 6x * 3x)) = 0
12 + -17x + 6x2 + -1(4 + -24x + (-3x + 18x2)) = 0

Combine like terms: -24x + -3x = -27x
12 + -17x + 6x2 + -1(4 + -27x + 18x2) = 0
12 + -17x + 6x2 + (4 * -1 + -27x * -1 + 18x2 * -1) = 0
12 + -17x + 6x2 + (-4 + 27x + -18x2) = 0

Reorder the terms:
12 + -4 + -17x + 27x + 6x2 + -18x2 = 0

Combine like terms: 12 + -4 = 8
8 + -17x + 27x + 6x2 + -18x2 = 0

Combine like terms: -17x + 27x = 10x
8 + 10x + 6x2 + -18x2 = 0

Combine like terms: 6x2 + -18x2 = -12x2
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((4 + -3x)(1 + 2x)) = 0

Ignore the factor 2.

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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