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

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


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

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

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

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

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

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

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

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

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

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

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

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

Add '2' to each side of the equation.
-2 + 2 + 6x = 0 + 2

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

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

Divide each side by '6'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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