(2x+8)(5x-1)=0

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Solution for (2x+8)(5x-1)=0 equation: 


Simplifying
(2x + 8)(5x + -1) = 0

Reorder the terms:
(8 + 2x)(5x + -1) = 0

Reorder the terms:
(8 + 2x)(-1 + 5x) = 0

Multiply (8 + 2x) * (-1 + 5x)
(8(-1 + 5x) + 2x * (-1 + 5x)) = 0
((-1 * 8 + 5x * 8) + 2x * (-1 + 5x)) = 0
((-8 + 40x) + 2x * (-1 + 5x)) = 0
(-8 + 40x + (-1 * 2x + 5x * 2x)) = 0
(-8 + 40x + (-2x + 10x2)) = 0

Combine like terms: 40x + -2x = 38x
(-8 + 38x + 10x2) = 0

Solving
-8 + 38x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 19x + 5x2) = 0

Factor a trinomial.
2((-4 + -1x)(1 + -5x)) = 0

Ignore the factor 2.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-4, 0.2}

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