(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.
(-10 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-10, 5}