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

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


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

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

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

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

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

Reorder the terms:
-12 + -1x + x2 = (-2 + x)(x + -1)

Reorder the terms:
-12 + -1x + x2 = (-2 + x)(-1 + x)

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

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

Add '-1x2' to each side of the equation.
-12 + -1x + x2 + -1x2 = 2 + -3x + x2 + -1x2

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

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

Solving
-12 + -1x = 2 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-12 + -1x + 3x = 2 + -3x + 3x

Combine like terms: -1x + 3x = 2x
-12 + 2x = 2 + -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + 2x = 2 + 0
-12 + 2x = 2

Add '12' to each side of the equation.
-12 + 12 + 2x = 2 + 12

Combine like terms: -12 + 12 = 0
0 + 2x = 2 + 12
2x = 2 + 12

Combine like terms: 2 + 12 = 14
2x = 14

Divide each side by '2'.
x = 7

Simplifying
x = 7

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