5(8x+3)(5x-2)=0

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Solution for 5(8x+3)(5x-2)=0 equation: 


Simplifying
5(8x + 3)(5x + -2) = 0

Reorder the terms:
5(3 + 8x)(5x + -2) = 0

Reorder the terms:
5(3 + 8x)(-2 + 5x) = 0

Multiply (3 + 8x) * (-2 + 5x)
5(3(-2 + 5x) + 8x * (-2 + 5x)) = 0
5((-2 * 3 + 5x * 3) + 8x * (-2 + 5x)) = 0
5((-6 + 15x) + 8x * (-2 + 5x)) = 0
5(-6 + 15x + (-2 * 8x + 5x * 8x)) = 0
5(-6 + 15x + (-16x + 40x2)) = 0

Combine like terms: 15x + -16x = -1x
5(-6 + -1x + 40x2) = 0
(-6 * 5 + -1x * 5 + 40x2 * 5) = 0
(-30 + -5x + 200x2) = 0

Solving
-30 + -5x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -1x + 40x2) = 0

Factor a trinomial.
5((-3 + -8x)(2 + -5x)) = 0

Ignore the factor 5.

Subproblem 1
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 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.375, 0.4}

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