6x(x+2)=3x(x+1)

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Solution for 6x(x+2)=3x(x+1) equation: 


Simplifying
6x(x + 2) = 3x(x + 1)

Reorder the terms:
6x(2 + x) = 3x(x + 1)
(2 * 6x + x * 6x) = 3x(x + 1)
(12x + 6x2) = 3x(x + 1)

Reorder the terms:
12x + 6x2 = 3x(1 + x)
12x + 6x2 = (1 * 3x + x * 3x)
12x + 6x2 = (3x + 3x2)

Solving
12x + 6x2 = 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
12x + -3x + 6x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 12x + -3x = 9x
9x + 6x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
9x + 3x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
9x + 3x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
9x + 3x2 = 0 + 3x2 + -3x2
9x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(3 + x) = 0

Ignore the factor 3.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {0, -3}

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