(x+3)(x+29)=360

Solution for (x+3)(x+29)=360 equation:

Simplifying
(x + 3)(x + 29) = 360

Reorder the terms:
(3 + x)(x + 29) = 360

Reorder the terms:
(3 + x)(29 + x) = 360

Multiply (3 + x) * (29 + x)
(3(29 + x) + x(29 + x)) = 360
((29 * 3 + x * 3) + x(29 + x)) = 360
((87 + 3x) + x(29 + x)) = 360
(87 + 3x + (29 * x + x * x)) = 360
(87 + 3x + (29x + x2)) = 360

Combine like terms: 3x + 29x = 32x
(87 + 32x + x2) = 360

Solving
87 + 32x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
87 + -360 + 32x + x2 = 360 + -360

Combine like terms: 87 + -360 = -273
-273 + 32x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-273 + 32x + x2 = 0

Factor a trinomial.
(-39 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-39 + -1x)' equal to zero and attempt to solve:

Simplifying
-39 + -1x = 0

Solving
-39 + -1x = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1x = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1x = 0 + 39
-1x = 0 + 39

Combine like terms: 0 + 39 = 39
-1x = 39

Divide each side by '-1'.
x = -39

Simplifying
x = -39
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-39, 7}