(3x-9)(6x+1)=0

Solution for (3x-9)(6x+1)=0 equation:

Simplifying
(3x + -9)(6x + 1) = 0

Reorder the terms:
(-9 + 3x)(6x + 1) = 0

Reorder the terms:
(-9 + 3x)(1 + 6x) = 0

Multiply (-9 + 3x) * (1 + 6x)
(-9(1 + 6x) + 3x * (1 + 6x)) = 0
((1 * -9 + 6x * -9) + 3x * (1 + 6x)) = 0
((-9 + -54x) + 3x * (1 + 6x)) = 0
(-9 + -54x + (1 * 3x + 6x * 3x)) = 0
(-9 + -54x + (3x + 18x2)) = 0

Combine like terms: -54x + 3x = -51x
(-9 + -51x + 18x2) = 0

Solving
-9 + -51x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -17x + 6x2) = 0

Factor a trinomial.
3((-1 + -6x)(3 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.1666666667, 3}