(x+1)(x+3)=2(x+3)

Solution for (x+1)(x+3)=2(x+3) equation:

Simplifying
(x + 1)(x + 3) = 2(x + 3)

Reorder the terms:
(1 + x)(x + 3) = 2(x + 3)

Reorder the terms:
(1 + x)(3 + x) = 2(x + 3)

Multiply (1 + x) * (3 + x)
(1(3 + x) + x(3 + x)) = 2(x + 3)
((3 * 1 + x * 1) + x(3 + x)) = 2(x + 3)
((3 + 1x) + x(3 + x)) = 2(x + 3)
(3 + 1x + (3 * x + x * x)) = 2(x + 3)
(3 + 1x + (3x + x2)) = 2(x + 3)

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = 2(x + 3)

Reorder the terms:
3 + 4x + x2 = 2(3 + x)
3 + 4x + x2 = (3 * 2 + x * 2)
3 + 4x + x2 = (6 + 2x)

Solving
3 + 4x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
3 + -6 + 4x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 3 + -6 = -3
-3 + 4x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 4x + -2x = 2x
-3 + 2x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-3 + 2x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-3 + 2x + x2 = 0 + 2x + -2x
-3 + 2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 2x + x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-3, 1}