8x(8x-5)(5x+9)=0

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Solution for 8x(8x-5)(5x+9)=0 equation: 


Simplifying
8x(8x + -5)(5x + 9) = 0

Reorder the terms:
8x(-5 + 8x)(5x + 9) = 0

Reorder the terms:
8x(-5 + 8x)(9 + 5x) = 0

Multiply (-5 + 8x) * (9 + 5x)
8x(-5(9 + 5x) + 8x * (9 + 5x)) = 0
8x((9 * -5 + 5x * -5) + 8x * (9 + 5x)) = 0
8x((-45 + -25x) + 8x * (9 + 5x)) = 0
8x(-45 + -25x + (9 * 8x + 5x * 8x)) = 0
8x(-45 + -25x + (72x + 40x2)) = 0

Combine like terms: -25x + 72x = 47x
8x(-45 + 47x + 40x2) = 0
(-45 * 8x + 47x * 8x + 40x2 * 8x) = 0
(-360x + 376x2 + 320x3) = 0

Solving
-360x + 376x2 + 320x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-45 + 47x + 40x2) = 0

Factor a trinomial.
8x((-9 + -5x)(5 + -8x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625
Solution
x = {0, -1.8, 0.625}

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