(x-4)(x-1)=28

Solution for (x-4)(x-1)=28 equation:

Simplifying
(x + -4)(x + -1) = 28

Reorder the terms:
(-4 + x)(x + -1) = 28

Reorder the terms:
(-4 + x)(-1 + x) = 28

Multiply (-4 + x) * (-1 + x)
(-4(-1 + x) + x(-1 + x)) = 28
((-1 * -4 + x * -4) + x(-1 + x)) = 28
((4 + -4x) + x(-1 + x)) = 28
(4 + -4x + (-1 * x + x * x)) = 28
(4 + -4x + (-1x + x2)) = 28

Combine like terms: -4x + -1x = -5x
(4 + -5x + x2) = 28

Solving
4 + -5x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
4 + -28 + -5x + x2 = 28 + -28

Combine like terms: 4 + -28 = -24
-24 + -5x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-24 + -5x + x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -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 '(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
Solution
x = {-3, 8}