2(x-3)(9x+2)=0

Solution for 2(x-3)(9x+2)=0 equation:

Simplifying
2(x + -3)(9x + 2) = 0

Reorder the terms:
2(-3 + x)(9x + 2) = 0

Reorder the terms:
2(-3 + x)(2 + 9x) = 0

Multiply (-3 + x) * (2 + 9x)
2(-3(2 + 9x) + x(2 + 9x)) = 0
2((2 * -3 + 9x * -3) + x(2 + 9x)) = 0
2((-6 + -27x) + x(2 + 9x)) = 0
2(-6 + -27x + (2 * x + 9x * x)) = 0
2(-6 + -27x + (2x + 9x2)) = 0

Combine like terms: -27x + 2x = -25x
2(-6 + -25x + 9x2) = 0
(-6 * 2 + -25x * 2 + 9x2 * 2) = 0
(-12 + -50x + 18x2) = 0

Solving
-12 + -50x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -25x + 9x2) = 0

Factor a trinomial.
2((-2 + -9x)(3 + -1x)) = 0

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

Simplifying
-2 + -9x = 0

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

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

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

Divide each side by '-9'.
x = -0.2222222222

Simplifying
x = -0.2222222222
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 = {-0.2222222222, 3}