3x+x(x-2)=0

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Solution for 3x+x(x-2)=0 equation:


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

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

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

Solving
1x + x2 = 0

Solving for variable 'x'.

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

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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