(5+x)(3+x)=35

Solution for (5+x)(3+x)=35 equation:

Simplifying
(5 + x)(3 + x) = 35

Multiply (5 + x) * (3 + x)
(5(3 + x) + x(3 + x)) = 35
((3 * 5 + x * 5) + x(3 + x)) = 35
((15 + 5x) + x(3 + x)) = 35
(15 + 5x + (3 * x + x * x)) = 35
(15 + 5x + (3x + x2)) = 35

Combine like terms: 5x + 3x = 8x
(15 + 8x + x2) = 35

Solving
15 + 8x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
15 + -35 + 8x + x2 = 35 + -35

Combine like terms: 15 + -35 = -20
-20 + 8x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-20 + 8x + x2 = 0

Factor a trinomial.
(-10 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
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 = {-10, 2}