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

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

Simplifying
3(x + 1) = 1(x2 + -1)

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

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

Solving
3 + 3x = -1 + 1x2

Solving for variable 'x'.

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

Combine like terms: 3 + 1 = 4
4 + 3x + -1x2 = -1 + 1x2 + 1 + -1x2

Reorder the terms:
4 + 3x + -1x2 = -1 + 1 + 1x2 + -1x2

Combine like terms: -1 + 1 = 0
4 + 3x + -1x2 = 0 + 1x2 + -1x2
4 + 3x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
4 + 3x + -1x2 = 0

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {4, -1}