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

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


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

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

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

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

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

Solving
-2 + 1x + x2 = 2x

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-1 + -1x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-1, 2}

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