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

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

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

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

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

Reorder the terms for easier multiplication:
2 * 1(-6 + x)(9 + 2x) = 0

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

Multiply (-6 + x) * (9 + 2x)
2(-6(9 + 2x) + x(9 + 2x)) = 0
2((9 * -6 + 2x * -6) + x(9 + 2x)) = 0
2((-54 + -12x) + x(9 + 2x)) = 0
2(-54 + -12x + (9 * x + 2x * x)) = 0
2(-54 + -12x + (9x + 2x2)) = 0

Combine like terms: -12x + 9x = -3x
2(-54 + -3x + 2x2) = 0
(-54 * 2 + -3x * 2 + 2x2 * 2) = 0
(-108 + -6x + 4x2) = 0

Solving
-108 + -6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3x + 2x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4.5, 6}