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

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


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

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

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

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

Combine like terms: -2x + 9x = 7x
(-3 + 7x + 6x2) + -1(4 + -1x)(3 + -6x) = 2

Multiply (4 + -1x) * (3 + -6x)
-3 + 7x + 6x2 + -1(4(3 + -6x) + -1x * (3 + -6x)) = 2
-3 + 7x + 6x2 + -1((3 * 4 + -6x * 4) + -1x * (3 + -6x)) = 2
-3 + 7x + 6x2 + -1((12 + -24x) + -1x * (3 + -6x)) = 2
-3 + 7x + 6x2 + -1(12 + -24x + (3 * -1x + -6x * -1x)) = 2
-3 + 7x + 6x2 + -1(12 + -24x + (-3x + 6x2)) = 2

Combine like terms: -24x + -3x = -27x
-3 + 7x + 6x2 + -1(12 + -27x + 6x2) = 2
-3 + 7x + 6x2 + (12 * -1 + -27x * -1 + 6x2 * -1) = 2
-3 + 7x + 6x2 + (-12 + 27x + -6x2) = 2

Reorder the terms:
-3 + -12 + 7x + 27x + 6x2 + -6x2 = 2

Combine like terms: -3 + -12 = -15
-15 + 7x + 27x + 6x2 + -6x2 = 2

Combine like terms: 7x + 27x = 34x
-15 + 34x + 6x2 + -6x2 = 2

Combine like terms: 6x2 + -6x2 = 0
-15 + 34x + 0 = 2
-15 + 34x = 2

Solving
-15 + 34x = 2

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + 34x = 2 + 15

Combine like terms: -15 + 15 = 0
0 + 34x = 2 + 15
34x = 2 + 15

Combine like terms: 2 + 15 = 17
34x = 17

Divide each side by '34'.
x = 0.5

Simplifying
x = 0.5

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