(3x+1)(3x-9)=11

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Solution for (3x+1)(3x-9)=11 equation: 


Simplifying
(3x + 1)(3x + -9) = 11

Reorder the terms:
(1 + 3x)(3x + -9) = 11

Reorder the terms:
(1 + 3x)(-9 + 3x) = 11

Multiply (1 + 3x) * (-9 + 3x)
(1(-9 + 3x) + 3x * (-9 + 3x)) = 11
((-9 * 1 + 3x * 1) + 3x * (-9 + 3x)) = 11
((-9 + 3x) + 3x * (-9 + 3x)) = 11
(-9 + 3x + (-9 * 3x + 3x * 3x)) = 11
(-9 + 3x + (-27x + 9x2)) = 11

Combine like terms: 3x + -27x = -24x
(-9 + -24x + 9x2) = 11

Solving
-9 + -24x + 9x2 = 11

Solving for variable 'x'.

Reorder the terms:
-9 + -11 + -24x + 9x2 = 11 + -11

Combine like terms: -9 + -11 = -20
-20 + -24x + 9x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-20 + -24x + 9x2 = 0

Factor a trinomial.
(-2 + -3x)(10 + -3x) = 0


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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {-0.6666666667, 3.333333333}

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