(x-1)(x-4)=10

Solution for (x-1)(x-4)=10 equation:

Simplifying
(x + -1)(x + -4) = 10

Reorder the terms:
(-1 + x)(x + -4) = 10

Reorder the terms:
(-1 + x)(-4 + x) = 10

Multiply (-1 + x) * (-4 + x)
(-1(-4 + x) + x(-4 + x)) = 10
((-4 * -1 + x * -1) + x(-4 + x)) = 10
((4 + -1x) + x(-4 + x)) = 10
(4 + -1x + (-4 * x + x * x)) = 10
(4 + -1x + (-4x + x2)) = 10

Combine like terms: -1x + -4x = -5x
(4 + -5x + x2) = 10

Solving
4 + -5x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
4 + -10 + -5x + x2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + -5x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + -5x + x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -1x) = 0

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}