(3+x)(10+x)=60

Solution for (3+x)(10+x)=60 equation:

Simplifying
(3 + x)(10 + x) = 60

Multiply (3 + x) * (10 + x)
(3(10 + x) + x(10 + x)) = 60
((10 * 3 + x * 3) + x(10 + x)) = 60
((30 + 3x) + x(10 + x)) = 60
(30 + 3x + (10 * x + x * x)) = 60
(30 + 3x + (10x + x2)) = 60

Combine like terms: 3x + 10x = 13x
(30 + 13x + x2) = 60

Solving
30 + 13x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
30 + -60 + 13x + x2 = 60 + -60

Combine like terms: 30 + -60 = -30
-30 + 13x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-30 + 13x + x2 = 0

Factor a trinomial.
(-15 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15, 2}