(3+9x)(7+3x)=3+9x

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Solution for (3+9x)(7+3x)=3+9x equation: 


Simplifying
(3 + 9x)(7 + 3x) = 3 + 9x

Multiply (3 + 9x) * (7 + 3x)
(3(7 + 3x) + 9x * (7 + 3x)) = 3 + 9x
((7 * 3 + 3x * 3) + 9x * (7 + 3x)) = 3 + 9x
((21 + 9x) + 9x * (7 + 3x)) = 3 + 9x
(21 + 9x + (7 * 9x + 3x * 9x)) = 3 + 9x
(21 + 9x + (63x + 27x2)) = 3 + 9x

Combine like terms: 9x + 63x = 72x
(21 + 72x + 27x2) = 3 + 9x

Solving
21 + 72x + 27x2 = 3 + 9x

Solving for variable 'x'.

Reorder the terms:
21 + -3 + 72x + -9x + 27x2 = 3 + 9x + -3 + -9x

Combine like terms: 21 + -3 = 18
18 + 72x + -9x + 27x2 = 3 + 9x + -3 + -9x

Combine like terms: 72x + -9x = 63x
18 + 63x + 27x2 = 3 + 9x + -3 + -9x

Reorder the terms:
18 + 63x + 27x2 = 3 + -3 + 9x + -9x

Combine like terms: 3 + -3 = 0
18 + 63x + 27x2 = 0 + 9x + -9x
18 + 63x + 27x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
18 + 63x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(2 + 7x + 3x2) = 0

Factor a trinomial.
9((2 + x)(1 + 3x)) = 0

Ignore the factor 9.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-2, -0.3333333333}

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