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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-2 + 1x = -5 + -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.
-2 + 1x + x = -5 + -1x + x

Combine like terms: 1x + x = 2x
-2 + 2x = -5 + -1x + x

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

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

Combine like terms: -2 + 2 = 0
0 + 2x = -5 + 2
2x = -5 + 2

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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