6(2x-1)(x+9)=0

Solution for 6(2x-1)(x+9)=0 equation:

Simplifying
6(2x + -1)(x + 9) = 0

Reorder the terms:
6(-1 + 2x)(x + 9) = 0

Reorder the terms:
6(-1 + 2x)(9 + x) = 0

Multiply (-1 + 2x) * (9 + x)
6(-1(9 + x) + 2x * (9 + x)) = 0
6((9 * -1 + x * -1) + 2x * (9 + x)) = 0
6((-9 + -1x) + 2x * (9 + x)) = 0
6(-9 + -1x + (9 * 2x + x * 2x)) = 0
6(-9 + -1x + (18x + 2x2)) = 0

Combine like terms: -1x + 18x = 17x
6(-9 + 17x + 2x2) = 0
(-9 * 6 + 17x * 6 + 2x2 * 6) = 0
(-54 + 102x + 12x2) = 0

Solving
-54 + 102x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 17x + 2x2) = 0

Factor a trinomial.
6((-9 + -1x)(1 + -2x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 0.5}