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

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

Simplifying
z + 1 = 3(z2 + -1)

Reorder the terms:
1 + z = 3(z2 + -1)

Reorder the terms:
1 + z = 3(-1 + z2)
1 + z = (-1 * 3 + z2 * 3)
1 + z = (-3 + 3z2)

Solving
1 + z = -3 + 3z2

Solving for variable 'z'.

Reorder the terms:
1 + 3 + z + -3z2 = -3 + 3z2 + 3 + -3z2

Combine like terms: 1 + 3 = 4
4 + z + -3z2 = -3 + 3z2 + 3 + -3z2

Reorder the terms:
4 + z + -3z2 = -3 + 3 + 3z2 + -3z2

Combine like terms: -3 + 3 = 0
4 + z + -3z2 = 0 + 3z2 + -3z2
4 + z + -3z2 = 3z2 + -3z2

Combine like terms: 3z2 + -3z2 = 0
4 + z + -3z2 = 0

Factor a trinomial.
(4 + -3z)(1 + z) = 0

Subproblem 1
Set the factor '(4 + -3z)' equal to zero and attempt to solve:

Simplifying
4 + -3z = 0

Solving
4 + -3z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3z = 0 + -4
-3z = 0 + -4

Combine like terms: 0 + -4 = -4
-3z = -4

Divide each side by '-3'.
z = 1.333333333

Simplifying
z = 1.333333333
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {1.333333333, -1}