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

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


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

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

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

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

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

Reorder the terms:
-3 + 2x + x2 = (2 + x)(x + 3) + 1

Reorder the terms:
-3 + 2x + x2 = (2 + x)(3 + x) + 1

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

Combine like terms: 2x + 3x = 5x
-3 + 2x + x2 = (6 + 5x + x2) + 1

Reorder the terms:
-3 + 2x + x2 = 6 + 1 + 5x + x2

Combine like terms: 6 + 1 = 7
-3 + 2x + x2 = 7 + 5x + x2

Add '-1x2' to each side of the equation.
-3 + 2x + x2 + -1x2 = 7 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x + 0 = 7 + 5x + x2 + -1x2
-3 + 2x = 7 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x = 7 + 5x + 0
-3 + 2x = 7 + 5x

Solving
-3 + 2x = 7 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-3 + 2x + -5x = 7 + 5x + -5x

Combine like terms: 2x + -5x = -3x
-3 + -3x = 7 + 5x + -5x

Combine like terms: 5x + -5x = 0
-3 + -3x = 7 + 0
-3 + -3x = 7

Add '3' to each side of the equation.
-3 + 3 + -3x = 7 + 3

Combine like terms: -3 + 3 = 0
0 + -3x = 7 + 3
-3x = 7 + 3

Combine like terms: 7 + 3 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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