(x+4)(x+1)=40

Solution for (x+4)(x+1)=40 equation:

Simplifying
(x + 4)(x + 1) = 40

Reorder the terms:
(4 + x)(x + 1) = 40

Reorder the terms:
(4 + x)(1 + x) = 40

Multiply (4 + x) * (1 + x)
(4(1 + x) + x(1 + x)) = 40
((1 * 4 + x * 4) + x(1 + x)) = 40
((4 + 4x) + x(1 + x)) = 40
(4 + 4x + (1 * x + x * x)) = 40
(4 + 4x + (1x + x2)) = 40

Combine like terms: 4x + 1x = 5x
(4 + 5x + x2) = 40

Solving
4 + 5x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
4 + -40 + 5x + x2 = 40 + -40

Combine like terms: 4 + -40 = -36
-36 + 5x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-9, 4}