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

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

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

Reorder the terms:
x(1 + x) = 3(x + 1)
(1 * x + x * x) = 3(x + 1)
(1x + x2) = 3(x + 1)

Reorder the terms:
1x + x2 = 3(1 + x)
1x + x2 = (1 * 3 + x * 3)
1x + x2 = (3 + 3x)

Solving
1x + x2 = 3 + 3x

Solving for variable 'x'.

Reorder the terms:
-3 + 1x + -3x + x2 = 3 + 3x + -3 + -3x

Combine like terms: 1x + -3x = -2x
-3 + -2x + x2 = 3 + 3x + -3 + -3x

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

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

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

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

Subproblem 1
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
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 = {-1, 3}