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

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


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

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

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

Multiply (-5 + 8x) * (5 + 2x)
(-5(5 + 2x) + 8x * (5 + 2x)) = 0
((5 * -5 + 2x * -5) + 8x * (5 + 2x)) = 0
((-25 + -10x) + 8x * (5 + 2x)) = 0
(-25 + -10x + (5 * 8x + 2x * 8x)) = 0
(-25 + -10x + (40x + 16x2)) = 0

Combine like terms: -10x + 40x = 30x
(-25 + 30x + 16x2) = 0

Solving
-25 + 30x + 16x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-5 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
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 = {-2.5, 0.625}

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