(x-5)(x-4)-(x+1)(x-2)=7

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Solution for (x-5)(x-4)-(x+1)(x-2)=7 equation: 


Simplifying
(x + -5)(x + -4) + -1(x + 1)(x + -2) = 7

Reorder the terms:
(-5 + x)(x + -4) + -1(x + 1)(x + -2) = 7

Reorder the terms:
(-5 + x)(-4 + x) + -1(x + 1)(x + -2) = 7

Multiply (-5 + x) * (-4 + x)
(-5(-4 + x) + x(-4 + x)) + -1(x + 1)(x + -2) = 7
((-4 * -5 + x * -5) + x(-4 + x)) + -1(x + 1)(x + -2) = 7
((20 + -5x) + x(-4 + x)) + -1(x + 1)(x + -2) = 7
(20 + -5x + (-4 * x + x * x)) + -1(x + 1)(x + -2) = 7
(20 + -5x + (-4x + x2)) + -1(x + 1)(x + -2) = 7

Combine like terms: -5x + -4x = -9x
(20 + -9x + x2) + -1(x + 1)(x + -2) = 7

Reorder the terms:
20 + -9x + x2 + -1(1 + x)(x + -2) = 7

Reorder the terms:
20 + -9x + x2 + -1(1 + x)(-2 + x) = 7

Multiply (1 + x) * (-2 + x)
20 + -9x + x2 + -1(1(-2 + x) + x(-2 + x)) = 7
20 + -9x + x2 + -1((-2 * 1 + x * 1) + x(-2 + x)) = 7
20 + -9x + x2 + -1((-2 + 1x) + x(-2 + x)) = 7
20 + -9x + x2 + -1(-2 + 1x + (-2 * x + x * x)) = 7
20 + -9x + x2 + -1(-2 + 1x + (-2x + x2)) = 7

Combine like terms: 1x + -2x = -1x
20 + -9x + x2 + -1(-2 + -1x + x2) = 7
20 + -9x + x2 + (-2 * -1 + -1x * -1 + x2 * -1) = 7
20 + -9x + x2 + (2 + 1x + -1x2) = 7

Reorder the terms:
20 + 2 + -9x + 1x + x2 + -1x2 = 7

Combine like terms: 20 + 2 = 22
22 + -9x + 1x + x2 + -1x2 = 7

Combine like terms: -9x + 1x = -8x
22 + -8x + x2 + -1x2 = 7

Combine like terms: x2 + -1x2 = 0
22 + -8x + 0 = 7
22 + -8x = 7

Solving
22 + -8x = 7

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + -8x = 7 + -22

Combine like terms: 22 + -22 = 0
0 + -8x = 7 + -22
-8x = 7 + -22

Combine like terms: 7 + -22 = -15
-8x = -15

Divide each side by '-8'.
x = 1.875

Simplifying
x = 1.875

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