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

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


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

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

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

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

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

Reorder the terms:
3 + -4x + x2 = (3 + x)(x + -4)

Reorder the terms:
3 + -4x + x2 = (3 + x)(-4 + x)

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

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

Add '-1x2' to each side of the equation.
3 + -4x + x2 + -1x2 = -12 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x + 0 = -12 + -1x + x2 + -1x2
3 + -4x = -12 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x = -12 + -1x + 0
3 + -4x = -12 + -1x

Solving
3 + -4x = -12 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
3 + -4x + x = -12 + -1x + x

Combine like terms: -4x + x = -3x
3 + -3x = -12 + -1x + x

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

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

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

Combine like terms: -12 + -3 = -15
-3x = -15

Divide each side by '-3'.
x = 5

Simplifying
x = 5

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