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

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


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

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

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

Multiply (-5 + 2x) * (-5 + 8x)
3(-5(-5 + 8x) + 2x * (-5 + 8x)) = 0
3((-5 * -5 + 8x * -5) + 2x * (-5 + 8x)) = 0
3((25 + -40x) + 2x * (-5 + 8x)) = 0
3(25 + -40x + (-5 * 2x + 8x * 2x)) = 0
3(25 + -40x + (-10x + 16x2)) = 0

Combine like terms: -40x + -10x = -50x
3(25 + -50x + 16x2) = 0
(25 * 3 + -50x * 3 + 16x2 * 3) = 0
(75 + -150x + 48x2) = 0

Solving
75 + -150x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -50x + 16x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {0.625, 2.5}

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