5x(5x-9)(8x+3)=0

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Solution for 5x(5x-9)(8x+3)=0 equation: 


Simplifying
5x(5x + -9)(8x + 3) = 0

Reorder the terms:
5x(-9 + 5x)(8x + 3) = 0

Reorder the terms:
5x(-9 + 5x)(3 + 8x) = 0

Multiply (-9 + 5x) * (3 + 8x)
5x(-9(3 + 8x) + 5x * (3 + 8x)) = 0
5x((3 * -9 + 8x * -9) + 5x * (3 + 8x)) = 0
5x((-27 + -72x) + 5x * (3 + 8x)) = 0
5x(-27 + -72x + (3 * 5x + 8x * 5x)) = 0
5x(-27 + -72x + (15x + 40x2)) = 0

Combine like terms: -72x + 15x = -57x
5x(-27 + -57x + 40x2) = 0
(-27 * 5x + -57x * 5x + 40x2 * 5x) = 0
(-135x + -285x2 + 200x3) = 0

Solving
-135x + -285x2 + 200x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-27 + -57x + 40x2) = 0

Factor a trinomial.
5x((-3 + -8x)(9 + -5x)) = 0

Ignore the factor 5.

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 '(-3 + -8x)' equal to zero and attempt to solve:

Simplifying
-3 + -8x = 0

Solving
-3 + -8x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x = 0 + 3
-8x = 0 + 3

Combine like terms: 0 + 3 = 3
-8x = 3

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375

Subproblem 3
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
Solution
x = {0, -0.375, 1.8}

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