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

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

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

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

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

Multiply (-10 + x) * (1 + 8x)
(-10(1 + 8x) + x(1 + 8x)) = 0
((1 * -10 + 8x * -10) + x(1 + 8x)) = 0
((-10 + -80x) + x(1 + 8x)) = 0
(-10 + -80x + (1 * x + 8x * x)) = 0
(-10 + -80x + (1x + 8x2)) = 0

Combine like terms: -80x + 1x = -79x
(-10 + -79x + 8x2) = 0

Solving
-10 + -79x + 8x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -8x = 0

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

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

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

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-0.125, 10}