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

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


Simplifying
3(2 + x) + -3x(3 + x) = 2(3 + x)
(2 * 3 + x * 3) + -3x(3 + x) = 2(3 + x)
(6 + 3x) + -3x(3 + x) = 2(3 + x)
6 + 3x + (3 * -3x + x * -3x) = 2(3 + x)
6 + 3x + (-9x + -3x2) = 2(3 + x)

Combine like terms: 3x + -9x = -6x
6 + -6x + -3x2 = 2(3 + x)
6 + -6x + -3x2 = (3 * 2 + x * 2)
6 + -6x + -3x2 = (6 + 2x)

Add '-6' to each side of the equation.
6 + -6x + -6 + -3x2 = 6 + -6 + 2x

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

Combine like terms: 6 + -6 = 0
0 + -6x + -3x2 = 6 + -6 + 2x
-6x + -3x2 = 6 + -6 + 2x

Combine like terms: 6 + -6 = 0
-6x + -3x2 = 0 + 2x
-6x + -3x2 = 2x

Solving
-6x + -3x2 = 2x

Solving for variable 'x'.

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

Combine like terms: -6x + -2x = -8x
-8x + -3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-8x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(8 + 3x) = 0

Ignore the factor -1.

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 '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {0, -2.666666667}

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