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

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


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

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

Reorder the terms:
-1x + x2 = x + 2(-2 + x)
-1x + x2 = x + (-2 * 2 + x * 2)
-1x + x2 = x + (-4 + 2x)

Reorder the terms:
-1x + x2 = -4 + x + 2x

Combine like terms: x + 2x = 3x
-1x + x2 = -4 + 3x

Solving
-1x + x2 = -4 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + -1x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: -1x + -3x = -4x
4 + -4x + x2 = -4 + 3x + 4 + -3x

Reorder the terms:
4 + -4x + x2 = -4 + 4 + 3x + -3x

Combine like terms: -4 + 4 = 0
4 + -4x + x2 = 0 + 3x + -3x
4 + -4x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -4x + x2 = 0

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

Subproblem 1

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

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 = {2, 2}

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