x(x+1)+x(x-2)=0

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Solution for x(x+1)+x(x-2)=0 equation:


Simplifying
x(x + 1) + x(x + -2) = 0

Reorder the terms:
x(1 + x) + x(x + -2) = 0
(1 * x + x * x) + x(x + -2) = 0
(1x + x2) + x(x + -2) = 0

Reorder the terms:
1x + x2 + x(-2 + x) = 0
1x + x2 + (-2 * x + x * x) = 0
1x + x2 + (-2x + x2) = 0

Reorder the terms:
1x + -2x + x2 + x2 = 0

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

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

Solving
-1x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x) = 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 + 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

Solution

x = {0, 0.5}

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