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

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


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

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

Reorder the terms:
12x + 2x2 = 3x(-3 + x)
12x + 2x2 = (-3 * 3x + x * 3x)
12x + 2x2 = (-9x + 3x2)

Solving
12x + 2x2 = -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
12x + 9x + 2x2 + -3x2 = -9x + 3x2 + 9x + -3x2

Combine like terms: 12x + 9x = 21x
21x + 2x2 + -3x2 = -9x + 3x2 + 9x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
21x + -1x2 = -9x + 3x2 + 9x + -3x2

Reorder the terms:
21x + -1x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
21x + -1x2 = 0 + 3x2 + -3x2
21x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
21x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(21 + -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 '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {0, 21}

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