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

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


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

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

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

Combine like terms: 40x + -1x = 39x
(8 + 39x + -5x2) = 0

Solving
8 + 39x + -5x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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 = {8, -0.2}

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