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

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

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

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

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

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

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

Solving
0 = -6 + -25x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 25x + -9x2 = -6 + -25x + 9x2 + 6 + 25x + -9x2

Reorder the terms:
6 + 25x + -9x2 = -6 + 6 + -25x + 25x + 9x2 + -9x2

Combine like terms: -6 + 6 = 0
6 + 25x + -9x2 = 0 + -25x + 25x + 9x2 + -9x2
6 + 25x + -9x2 = -25x + 25x + 9x2 + -9x2

Combine like terms: -25x + 25x = 0
6 + 25x + -9x2 = 0 + 9x2 + -9x2
6 + 25x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
6 + 25x + -9x2 = 0

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

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 + 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
Solution
x = {3, -0.2222222222}