3x(x+2)=2x(x+1)+0

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Solution for 3x(x+2)=2x(x+1)+0 equation: 


Simplifying
3x(x + 2) = 2x(x + 1) + 0

Reorder the terms:
3x(2 + x) = 2x(x + 1) + 0
(2 * 3x + x * 3x) = 2x(x + 1) + 0
(6x + 3x2) = 2x(x + 1) + 0

Reorder the terms:
6x + 3x2 = 2x(1 + x) + 0
6x + 3x2 = (1 * 2x + x * 2x) + 0
6x + 3x2 = (2x + 2x2) + 0

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

Solving
6x + 3x2 = 2x + 2x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2x + -2x = 0
4x + 1x2 = 0 + 2x2 + -2x2
4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, -4}

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