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

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


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

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

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

Multiply (2 + 3x) * (-9 + x)
0 = (2(-9 + x) + 3x * (-9 + x))
0 = ((-9 * 2 + x * 2) + 3x * (-9 + x))
0 = ((-18 + 2x) + 3x * (-9 + x))
0 = (-18 + 2x + (-9 * 3x + x * 3x))
0 = (-18 + 2x + (-27x + 3x2))

Combine like terms: 2x + -27x = -25x
0 = (-18 + -25x + 3x2)

Solving
0 = -18 + -25x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 18 = 18
18 + 25x + -3x2 = -18 + -25x + 3x2 + 18 + 25x + -3x2

Reorder the terms:
18 + 25x + -3x2 = -18 + 18 + -25x + 25x + 3x2 + -3x2

Combine like terms: -18 + 18 = 0
18 + 25x + -3x2 = 0 + -25x + 25x + 3x2 + -3x2
18 + 25x + -3x2 = -25x + 25x + 3x2 + -3x2

Combine like terms: -25x + 25x = 0
18 + 25x + -3x2 = 0 + 3x2 + -3x2
18 + 25x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18 + 25x + -3x2 = 0

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


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 '(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 = {9, -0.6666666667}

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