(x-5)(x-8)=10

Solution for (x-5)(x-8)=10 equation:

Simplifying
(x + -5)(x + -8) = 10

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

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

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

Combine like terms: -5x + -8x = -13x
(40 + -13x + x2) = 10

Solving
40 + -13x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
40 + -10 + -13x + x2 = 10 + -10

Combine like terms: 40 + -10 = 30
30 + -13x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
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 = {3, 10}