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

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


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

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

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

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) = (x + -1)(x + 1)
((5 * -2 + x * -2) + x(5 + x)) = (x + -1)(x + 1)
((-10 + -2x) + x(5 + x)) = (x + -1)(x + 1)
(-10 + -2x + (5 * x + x * x)) = (x + -1)(x + 1)
(-10 + -2x + (5x + x2)) = (x + -1)(x + 1)

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) = (x + -1)(x + 1)

Reorder the terms:
-10 + 3x + x2 = (-1 + x)(x + 1)

Reorder the terms:
-10 + 3x + x2 = (-1 + x)(1 + x)

Multiply (-1 + x) * (1 + x)
-10 + 3x + x2 = (-1(1 + x) + x(1 + x))
-10 + 3x + x2 = ((1 * -1 + x * -1) + x(1 + x))
-10 + 3x + x2 = ((-1 + -1x) + x(1 + x))
-10 + 3x + x2 = (-1 + -1x + (1 * x + x * x))
-10 + 3x + x2 = (-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
-10 + 3x + x2 = (-1 + 0 + x2)
-10 + 3x + x2 = (-1 + x2)

Add '-1x2' to each side of the equation.
-10 + 3x + x2 + -1x2 = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x + 0 = -1 + x2 + -1x2
-10 + 3x = -1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x = -1 + 0
-10 + 3x = -1

Solving
-10 + 3x = -1

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + 3x = -1 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = -1 + 10
3x = -1 + 10

Combine like terms: -1 + 10 = 9
3x = 9

Divide each side by '3'.
x = 3

Simplifying
x = 3

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