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

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

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

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

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

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

Combine like terms: -10x + -8x = -18x
(10 + -18x + 8x2) = 0

Solving
10 + -18x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -9x + 4x2) = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {1, 1.25}