(x+3)(x+7)=60

Solution for (x+3)(x+7)=60 equation:

Simplifying
(x + 3)(x + 7) = 60

Reorder the terms:
(3 + x)(x + 7) = 60

Reorder the terms:
(3 + x)(7 + x) = 60

Multiply (3 + x) * (7 + x)
(3(7 + x) + x(7 + x)) = 60
((7 * 3 + x * 3) + x(7 + x)) = 60
((21 + 3x) + x(7 + x)) = 60
(21 + 3x + (7 * x + x * x)) = 60
(21 + 3x + (7x + x2)) = 60

Combine like terms: 3x + 7x = 10x
(21 + 10x + x2) = 60

Solving
21 + 10x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
21 + -60 + 10x + x2 = 60 + -60

Combine like terms: 21 + -60 = -39
-39 + 10x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-39 + 10x + x2 = 0

Factor a trinomial.
(-13 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-13, 3}