(3x)(2x)+6=3x+9

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Solution for (3x)(2x)+6=3x+9 equation: 


Simplifying
(3x)(2x) + 6 = 3x + 9

Remove parenthesis around (3x)
3x(2x) + 6 = 3x + 9

Remove parenthesis around (2x)
3x * 2x + 6 = 3x + 9

Reorder the terms for easier multiplication:
3 * 2x * x + 6 = 3x + 9

Multiply 3 * 2
6x * x + 6 = 3x + 9

Multiply x * x
6x2 + 6 = 3x + 9

Reorder the terms:
6 + 6x2 = 3x + 9

Reorder the terms:
6 + 6x2 = 9 + 3x

Solving
6 + 6x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
6 + -9 + -3x + 6x2 = 9 + 3x + -9 + -3x

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

Reorder the terms:
-3 + -3x + 6x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-3 + -3x + 6x2 = 0 + 3x + -3x
-3 + -3x + 6x2 = 3x + -3x

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -1x + 2x2) = 0

Factor a trinomial.
3((-1 + -2x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.5, 1}

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