0=(x+9)(3x+1)

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Solution for 0=(x+9)(3x+1) equation: 


Simplifying
0 = (x + 9)(3x + 1)

Reorder the terms:
0 = (9 + x)(3x + 1)

Reorder the terms:
0 = (9 + x)(1 + 3x)

Multiply (9 + x) * (1 + 3x)
0 = (9(1 + 3x) + x(1 + 3x))
0 = ((1 * 9 + 3x * 9) + x(1 + 3x))
0 = ((9 + 27x) + x(1 + 3x))
0 = (9 + 27x + (1 * x + 3x * x))
0 = (9 + 27x + (1x + 3x2))

Combine like terms: 27x + 1x = 28x
0 = (9 + 28x + 3x2)

Solving
0 = 9 + 28x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + -28x + -3x2 = 9 + 28x + 3x2 + -9 + -28x + -3x2

Reorder the terms:
-9 + -28x + -3x2 = 9 + -9 + 28x + -28x + 3x2 + -3x2

Combine like terms: 9 + -9 = 0
-9 + -28x + -3x2 = 0 + 28x + -28x + 3x2 + -3x2
-9 + -28x + -3x2 = 28x + -28x + 3x2 + -3x2

Combine like terms: 28x + -28x = 0
-9 + -28x + -3x2 = 0 + 3x2 + -3x2
-9 + -28x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9 + -28x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 28x + 3x2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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 = {-9, -0.3333333333}

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