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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