(x+5)(x+2)=54

Solution for (x+5)(x+2)=54 equation:

Simplifying
(x + 5)(x + 2) = 54

Reorder the terms:
(5 + x)(x + 2) = 54

Reorder the terms:
(5 + x)(2 + x) = 54

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = 54
((2 * 5 + x * 5) + x(2 + x)) = 54
((10 + 5x) + x(2 + x)) = 54
(10 + 5x + (2 * x + x * x)) = 54
(10 + 5x + (2x + x2)) = 54

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = 54

Solving
10 + 7x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
10 + -54 + 7x + x2 = 54 + -54

Combine like terms: 10 + -54 = -44
-44 + 7x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-44 + 7x + x2 = 0

Factor a trinomial.
(-11 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
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 = {-11, 4}