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

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


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

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

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

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

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

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

Solving
5x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 5}

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