(x-1)(x+2)=x^2-5(x+3)

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Solution for (x-1)(x+2)=x^2-5(x+3) equation: 


Simplifying
(x + -1)(x + 2) = x2 + -5(x + 3)

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

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

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = x2 + -5(x + 3)
((2 * -1 + x * -1) + x(2 + x)) = x2 + -5(x + 3)
((-2 + -1x) + x(2 + x)) = x2 + -5(x + 3)
(-2 + -1x + (2 * x + x * x)) = x2 + -5(x + 3)
(-2 + -1x + (2x + x2)) = x2 + -5(x + 3)

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

Reorder the terms:
-2 + 1x + x2 = x2 + -5(3 + x)
-2 + 1x + x2 = x2 + (3 * -5 + x * -5)
-2 + 1x + x2 = x2 + (-15 + -5x)

Reorder the terms:
-2 + 1x + x2 = -15 + -5x + x2

Add '-1x2' to each side of the equation.
-2 + 1x + x2 + -1x2 = -15 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 0 = -15 + -5x + x2 + -1x2
-2 + 1x = -15 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x = -15 + -5x + 0
-2 + 1x = -15 + -5x

Solving
-2 + 1x = -15 + -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.
-2 + 1x + 5x = -15 + -5x + 5x

Combine like terms: 1x + 5x = 6x
-2 + 6x = -15 + -5x + 5x

Combine like terms: -5x + 5x = 0
-2 + 6x = -15 + 0
-2 + 6x = -15

Add '2' to each side of the equation.
-2 + 2 + 6x = -15 + 2

Combine like terms: -2 + 2 = 0
0 + 6x = -15 + 2
6x = -15 + 2

Combine like terms: -15 + 2 = -13
6x = -13

Divide each side by '6'.
x = -2.166666667

Simplifying
x = -2.166666667

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