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

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


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

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

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

Solving
3x + 3x2 = 12x + 2x2

Solving for variable 'x'.

Reorder the terms:
3x + -12x + 3x2 + -2x2 = 12x + 2x2 + -12x + -2x2

Combine like terms: 3x + -12x = -9x
-9x + 3x2 + -2x2 = 12x + 2x2 + -12x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-9x + 1x2 = 12x + 2x2 + -12x + -2x2

Reorder the terms:
-9x + 1x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-9x + 1x2 = 0 + 2x2 + -2x2
-9x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-9x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + 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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

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

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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