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

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Solution for (x-2)(x-3)-(x+1)(x-4)=0 equation: 


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

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

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

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

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) + -1(x + 1)(x + -4) = 0

Reorder the terms:
6 + -5x + x2 + -1(1 + x)(x + -4) = 0

Reorder the terms:
6 + -5x + x2 + -1(1 + x)(-4 + x) = 0

Multiply (1 + x) * (-4 + x)
6 + -5x + x2 + -1(1(-4 + x) + x(-4 + x)) = 0
6 + -5x + x2 + -1((-4 * 1 + x * 1) + x(-4 + x)) = 0
6 + -5x + x2 + -1((-4 + 1x) + x(-4 + x)) = 0
6 + -5x + x2 + -1(-4 + 1x + (-4 * x + x * x)) = 0
6 + -5x + x2 + -1(-4 + 1x + (-4x + x2)) = 0

Combine like terms: 1x + -4x = -3x
6 + -5x + x2 + -1(-4 + -3x + x2) = 0
6 + -5x + x2 + (-4 * -1 + -3x * -1 + x2 * -1) = 0
6 + -5x + x2 + (4 + 3x + -1x2) = 0

Reorder the terms:
6 + 4 + -5x + 3x + x2 + -1x2 = 0

Combine like terms: 6 + 4 = 10
10 + -5x + 3x + x2 + -1x2 = 0

Combine like terms: -5x + 3x = -2x
10 + -2x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
10 + -2x + 0 = 0
10 + -2x = 0

Solving
10 + -2x = 0

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + -2x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -2x = 0 + -10
-2x = 0 + -10

Combine like terms: 0 + -10 = -10
-2x = -10

Divide each side by '-2'.
x = 5

Simplifying
x = 5

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