2x(x-2)=x+3

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


Simplifying
2x(x + -2) = x + 3

Reorder the terms:
2x(-2 + x) = x + 3
(-2 * 2x + x * 2x) = x + 3
(-4x + 2x2) = x + 3

Reorder the terms:
-4x + 2x2 = 3 + x

Solving
-4x + 2x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -4x + -1x + 2x2 = 3 + x + -3 + -1x

Combine like terms: -4x + -1x = -5x
-3 + -5x + 2x2 = 3 + x + -3 + -1x

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

Combine like terms: 3 + -3 = 0
-3 + -5x + 2x2 = 0 + x + -1x
-3 + -5x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + -5x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-0.5, 3}

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