(2x-1)(3x-2)=12

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Solution for (2x-1)(3x-2)=12 equation: 


Simplifying
(2x + -1)(3x + -2) = 12

Reorder the terms:
(-1 + 2x)(3x + -2) = 12

Reorder the terms:
(-1 + 2x)(-2 + 3x) = 12

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

Combine like terms: -3x + -4x = -7x
(2 + -7x + 6x2) = 12

Solving
2 + -7x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
2 + -12 + -7x + 6x2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + -7x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + -7x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.8333333333, 2}

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