(x+1)(x+3)=35

Solution for (x+1)(x+3)=35 equation:

Simplifying
(x + 1)(x + 3) = 35

Reorder the terms:
(1 + x)(x + 3) = 35

Reorder the terms:
(1 + x)(3 + x) = 35

Multiply (1 + x) * (3 + x)
(1(3 + x) + x(3 + x)) = 35
((3 * 1 + x * 1) + x(3 + x)) = 35
((3 + 1x) + x(3 + x)) = 35
(3 + 1x + (3 * x + x * x)) = 35
(3 + 1x + (3x + x2)) = 35

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = 35

Solving
3 + 4x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
3 + -35 + 4x + x2 = 35 + -35

Combine like terms: 3 + -35 = -32
-32 + 4x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-32 + 4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 4}