0=(6x-18)(3x+2)

Solution for 0=(6x-18)(3x+2) equation:

Simplifying
0 = (6x + -18)(3x + 2)

Reorder the terms:
0 = (-18 + 6x)(3x + 2)

Reorder the terms:
0 = (-18 + 6x)(2 + 3x)

Multiply (-18 + 6x) * (2 + 3x)
0 = (-18(2 + 3x) + 6x * (2 + 3x))
0 = ((2 * -18 + 3x * -18) + 6x * (2 + 3x))
0 = ((-36 + -54x) + 6x * (2 + 3x))
0 = (-36 + -54x + (2 * 6x + 3x * 6x))
0 = (-36 + -54x + (12x + 18x2))

Combine like terms: -54x + 12x = -42x
0 = (-36 + -42x + 18x2)

Solving
0 = -36 + -42x + 18x2

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + 42x + -18x2 = -36 + -42x + 18x2 + 36 + 42x + -18x2

Reorder the terms:
36 + 42x + -18x2 = -36 + 36 + -42x + 42x + 18x2 + -18x2

Combine like terms: -36 + 36 = 0
36 + 42x + -18x2 = 0 + -42x + 42x + 18x2 + -18x2
36 + 42x + -18x2 = -42x + 42x + 18x2 + -18x2

Combine like terms: -42x + 42x = 0
36 + 42x + -18x2 = 0 + 18x2 + -18x2
36 + 42x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
36 + 42x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 7x + -3x2) = 0

Factor a trinomial.
6((3 + -1x)(2 + 3x)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
x = {3, -0.6666666667}