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

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


Simplifying
(x + -2) * x + (x + 2) * 3x = 0

Reorder the terms:
(-2 + x) * x + (x + 2) * 3x = 0

Reorder the terms for easier multiplication:
x(-2 + x) + (x + 2) * 3x = 0
(-2 * x + x * x) + (x + 2) * 3x = 0
(-2x + x2) + (x + 2) * 3x = 0

Reorder the terms:
-2x + x2 + (2 + x) * 3x = 0

Reorder the terms for easier multiplication:
-2x + x2 + 3x(2 + x) = 0
-2x + x2 + (2 * 3x + x * 3x) = 0
-2x + x2 + (6x + 3x2) = 0

Reorder the terms:
-2x + 6x + x2 + 3x2 = 0

Combine like terms: -2x + 6x = 4x
4x + x2 + 3x2 = 0

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

Solving
4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + x) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0, -1}

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