(5x+9)(3x-2)=0

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Solution for (5x+9)(3x-2)=0 equation: 


Simplifying
(5x + 9)(3x + -2) = 0

Reorder the terms:
(9 + 5x)(3x + -2) = 0

Reorder the terms:
(9 + 5x)(-2 + 3x) = 0

Multiply (9 + 5x) * (-2 + 3x)
(9(-2 + 3x) + 5x * (-2 + 3x)) = 0
((-2 * 9 + 3x * 9) + 5x * (-2 + 3x)) = 0
((-18 + 27x) + 5x * (-2 + 3x)) = 0
(-18 + 27x + (-2 * 5x + 3x * 5x)) = 0
(-18 + 27x + (-10x + 15x2)) = 0

Combine like terms: 27x + -10x = 17x
(-18 + 17x + 15x2) = 0

Solving
-18 + 17x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -5x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -5x)' equal to zero and attempt to solve:

Simplifying
-9 + -5x = 0

Solving
-9 + -5x = 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 + -5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x = 0 + 9
-5x = 0 + 9

Combine like terms: 0 + 9 = 9
-5x = 9

Divide each side by '-5'.
x = -1.8

Simplifying
x = -1.8

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 = {-1.8, 0.6666666667}

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