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

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


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

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

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

Multiply (-2 + 3x) * (9 + 2x)
(-2(9 + 2x) + 3x * (9 + 2x)) = 0
((9 * -2 + 2x * -2) + 3x * (9 + 2x)) = 0
((-18 + -4x) + 3x * (9 + 2x)) = 0
(-18 + -4x + (9 * 3x + 2x * 3x)) = 0
(-18 + -4x + (27x + 6x2)) = 0

Combine like terms: -4x + 27x = 23x
(-18 + 23x + 6x2) = 0

Solving
-18 + 23x + 6x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-4.5, 0.6666666667}

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