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

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


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

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

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

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) + -1(1 + -1x)(2 + -1x) = 0
((-4 * -3 + x * -3) + x(-4 + x)) + -1(1 + -1x)(2 + -1x) = 0
((12 + -3x) + x(-4 + x)) + -1(1 + -1x)(2 + -1x) = 0
(12 + -3x + (-4 * x + x * x)) + -1(1 + -1x)(2 + -1x) = 0
(12 + -3x + (-4x + x2)) + -1(1 + -1x)(2 + -1x) = 0

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) + -1(1 + -1x)(2 + -1x) = 0

Multiply (1 + -1x) * (2 + -1x)
12 + -7x + x2 + -1(1(2 + -1x) + -1x * (2 + -1x)) = 0
12 + -7x + x2 + -1((2 * 1 + -1x * 1) + -1x * (2 + -1x)) = 0
12 + -7x + x2 + -1((2 + -1x) + -1x * (2 + -1x)) = 0
12 + -7x + x2 + -1(2 + -1x + (2 * -1x + -1x * -1x)) = 0
12 + -7x + x2 + -1(2 + -1x + (-2x + 1x2)) = 0

Combine like terms: -1x + -2x = -3x
12 + -7x + x2 + -1(2 + -3x + 1x2) = 0
12 + -7x + x2 + (2 * -1 + -3x * -1 + 1x2 * -1) = 0
12 + -7x + x2 + (-2 + 3x + -1x2) = 0

Reorder the terms:
12 + -2 + -7x + 3x + x2 + -1x2 = 0

Combine like terms: 12 + -2 = 10
10 + -7x + 3x + x2 + -1x2 = 0

Combine like terms: -7x + 3x = -4x
10 + -4x + x2 + -1x2 = 0

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

Solving
10 + -4x = 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 + -4x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -4x = 0 + -10
-4x = 0 + -10

Combine like terms: 0 + -10 = -10
-4x = -10

Divide each side by '-4'.
x = 2.5

Simplifying
x = 2.5

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