(x-1)(x+3)=(x+2)(x+6)

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Solution for (x-1)(x+3)=(x+2)(x+6) equation: 


Simplifying
(x + -1)(x + 3) = (x + 2)(x + 6)

Reorder the terms:
(-1 + x)(x + 3) = (x + 2)(x + 6)

Reorder the terms:
(-1 + x)(3 + x) = (x + 2)(x + 6)

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

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

Reorder the terms:
-3 + 2x + x2 = (2 + x)(x + 6)

Reorder the terms:
-3 + 2x + x2 = (2 + x)(6 + x)

Multiply (2 + x) * (6 + x)
-3 + 2x + x2 = (2(6 + x) + x(6 + x))
-3 + 2x + x2 = ((6 * 2 + x * 2) + x(6 + x))
-3 + 2x + x2 = ((12 + 2x) + x(6 + x))
-3 + 2x + x2 = (12 + 2x + (6 * x + x * x))
-3 + 2x + x2 = (12 + 2x + (6x + x2))

Combine like terms: 2x + 6x = 8x
-3 + 2x + x2 = (12 + 8x + x2)

Add '-1x2' to each side of the equation.
-3 + 2x + x2 + -1x2 = 12 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x + 0 = 12 + 8x + x2 + -1x2
-3 + 2x = 12 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x = 12 + 8x + 0
-3 + 2x = 12 + 8x

Solving
-3 + 2x = 12 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
-3 + 2x + -8x = 12 + 8x + -8x

Combine like terms: 2x + -8x = -6x
-3 + -6x = 12 + 8x + -8x

Combine like terms: 8x + -8x = 0
-3 + -6x = 12 + 0
-3 + -6x = 12

Add '3' to each side of the equation.
-3 + 3 + -6x = 12 + 3

Combine like terms: -3 + 3 = 0
0 + -6x = 12 + 3
-6x = 12 + 3

Combine like terms: 12 + 3 = 15
-6x = 15

Divide each side by '-6'.
x = -2.5

Simplifying
x = -2.5

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