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

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


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

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

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

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

Combine like terms: -27x + 2x = -25x
5(-18 + -25x + 3x2) = 0
(-18 * 5 + -25x * 5 + 3x2 * 5) = 0
(-90 + -125x + 15x2) = 0

Solving
-90 + -125x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -25x + 3x2) = 0

Factor a trinomial.
5((-2 + -3x)(9 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.6666666667, 9}

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