(x-3)(x-4)=(x+5)(x-2)+x-12

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Solution for (x-3)(x-4)=(x+5)(x-2)+x-12 equation: 


Simplifying
(x + -3)(x + -4) = (x + 5)(x + -2) + x + -12

Reorder the terms:
(-3 + x)(x + -4) = (x + 5)(x + -2) + x + -12

Reorder the terms:
(-3 + x)(-4 + x) = (x + 5)(x + -2) + x + -12

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) = (x + 5)(x + -2) + x + -12
((-4 * -3 + x * -3) + x(-4 + x)) = (x + 5)(x + -2) + x + -12
((12 + -3x) + x(-4 + x)) = (x + 5)(x + -2) + x + -12
(12 + -3x + (-4 * x + x * x)) = (x + 5)(x + -2) + x + -12
(12 + -3x + (-4x + x2)) = (x + 5)(x + -2) + x + -12

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) = (x + 5)(x + -2) + x + -12

Reorder the terms:
12 + -7x + x2 = (5 + x)(x + -2) + x + -12

Reorder the terms:
12 + -7x + x2 = (5 + x)(-2 + x) + x + -12

Multiply (5 + x) * (-2 + x)
12 + -7x + x2 = (5(-2 + x) + x(-2 + x)) + x + -12
12 + -7x + x2 = ((-2 * 5 + x * 5) + x(-2 + x)) + x + -12
12 + -7x + x2 = ((-10 + 5x) + x(-2 + x)) + x + -12
12 + -7x + x2 = (-10 + 5x + (-2 * x + x * x)) + x + -12
12 + -7x + x2 = (-10 + 5x + (-2x + x2)) + x + -12

Combine like terms: 5x + -2x = 3x
12 + -7x + x2 = (-10 + 3x + x2) + x + -12

Reorder the terms:
12 + -7x + x2 = -10 + -12 + 3x + x + x2

Combine like terms: -10 + -12 = -22
12 + -7x + x2 = -22 + 3x + x + x2

Combine like terms: 3x + x = 4x
12 + -7x + x2 = -22 + 4x + x2

Add '-1x2' to each side of the equation.
12 + -7x + x2 + -1x2 = -22 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x + 0 = -22 + 4x + x2 + -1x2
12 + -7x = -22 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -7x = -22 + 4x + 0
12 + -7x = -22 + 4x

Solving
12 + -7x = -22 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
12 + -7x + -4x = -22 + 4x + -4x

Combine like terms: -7x + -4x = -11x
12 + -11x = -22 + 4x + -4x

Combine like terms: 4x + -4x = 0
12 + -11x = -22 + 0
12 + -11x = -22

Add '-12' to each side of the equation.
12 + -12 + -11x = -22 + -12

Combine like terms: 12 + -12 = 0
0 + -11x = -22 + -12
-11x = -22 + -12

Combine like terms: -22 + -12 = -34
-11x = -34

Divide each side by '-11'.
x = 3.090909091

Simplifying
x = 3.090909091

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