(2x-1)(x-2)-(x+3)(2x-7)=3

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Solution for (2x-1)(x-2)-(x+3)(2x-7)=3 equation: 


Simplifying
(2x + -1)(x + -2) + -1(x + 3)(2x + -7) = 3

Reorder the terms:
(-1 + 2x)(x + -2) + -1(x + 3)(2x + -7) = 3

Reorder the terms:
(-1 + 2x)(-2 + x) + -1(x + 3)(2x + -7) = 3

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

Combine like terms: -1x + -4x = -5x
(2 + -5x + 2x2) + -1(x + 3)(2x + -7) = 3

Reorder the terms:
2 + -5x + 2x2 + -1(3 + x)(2x + -7) = 3

Reorder the terms:
2 + -5x + 2x2 + -1(3 + x)(-7 + 2x) = 3

Multiply (3 + x) * (-7 + 2x)
2 + -5x + 2x2 + -1(3(-7 + 2x) + x(-7 + 2x)) = 3
2 + -5x + 2x2 + -1((-7 * 3 + 2x * 3) + x(-7 + 2x)) = 3
2 + -5x + 2x2 + -1((-21 + 6x) + x(-7 + 2x)) = 3
2 + -5x + 2x2 + -1(-21 + 6x + (-7 * x + 2x * x)) = 3
2 + -5x + 2x2 + -1(-21 + 6x + (-7x + 2x2)) = 3

Combine like terms: 6x + -7x = -1x
2 + -5x + 2x2 + -1(-21 + -1x + 2x2) = 3
2 + -5x + 2x2 + (-21 * -1 + -1x * -1 + 2x2 * -1) = 3
2 + -5x + 2x2 + (21 + 1x + -2x2) = 3

Reorder the terms:
2 + 21 + -5x + 1x + 2x2 + -2x2 = 3

Combine like terms: 2 + 21 = 23
23 + -5x + 1x + 2x2 + -2x2 = 3

Combine like terms: -5x + 1x = -4x
23 + -4x + 2x2 + -2x2 = 3

Combine like terms: 2x2 + -2x2 = 0
23 + -4x + 0 = 3
23 + -4x = 3

Solving
23 + -4x = 3

Solving for variable 'x'.

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

Add '-23' to each side of the equation.
23 + -23 + -4x = 3 + -23

Combine like terms: 23 + -23 = 0
0 + -4x = 3 + -23
-4x = 3 + -23

Combine like terms: 3 + -23 = -20
-4x = -20

Divide each side by '-4'.
x = 5

Simplifying
x = 5

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