(x-4)(x-1)=54

Solution for (x-4)(x-1)=54 equation:

Simplifying
(x + -4)(x + -1) = 54

Reorder the terms:
(-4 + x)(x + -1) = 54

Reorder the terms:
(-4 + x)(-1 + x) = 54

Multiply (-4 + x) * (-1 + x)
(-4(-1 + x) + x(-1 + x)) = 54
((-1 * -4 + x * -4) + x(-1 + x)) = 54
((4 + -4x) + x(-1 + x)) = 54
(4 + -4x + (-1 * x + x * x)) = 54
(4 + -4x + (-1x + x2)) = 54

Combine like terms: -4x + -1x = -5x
(4 + -5x + x2) = 54

Solving
4 + -5x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
4 + -54 + -5x + x2 = 54 + -54

Combine like terms: 4 + -54 = -50
-50 + -5x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-50 + -5x + x2 = 0

Factor a trinomial.
(-5 + -1x)(10 + -1x) = 0

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 10}