10(4x+1)(5x-8)=0

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Solution for 10(4x+1)(5x-8)=0 equation: 


Simplifying
10(4x + 1)(5x + -8) = 0

Reorder the terms:
10(1 + 4x)(5x + -8) = 0

Reorder the terms:
10(1 + 4x)(-8 + 5x) = 0

Multiply (1 + 4x) * (-8 + 5x)
10(1(-8 + 5x) + 4x * (-8 + 5x)) = 0
10((-8 * 1 + 5x * 1) + 4x * (-8 + 5x)) = 0
10((-8 + 5x) + 4x * (-8 + 5x)) = 0
10(-8 + 5x + (-8 * 4x + 5x * 4x)) = 0
10(-8 + 5x + (-32x + 20x2)) = 0

Combine like terms: 5x + -32x = -27x
10(-8 + -27x + 20x2) = 0
(-8 * 10 + -27x * 10 + 20x2 * 10) = 0
(-80 + -270x + 200x2) = 0

Solving
-80 + -270x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + -27x + 20x2) = 0

Factor a trinomial.
10((-1 + -4x)(8 + -5x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-0.25, 1.6}

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