3f=2(f^2-1)

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

Simplifying
3f = 2(f2 + -1)

Reorder the terms:
3f = 2(-1 + f2)
3f = (-1 * 2 + f2 * 2)
3f = (-2 + 2f2)

Solving
3f = -2 + 2f2

Solving for variable 'f'.

Reorder the terms:
2 + 3f + -2f2 = -2 + 2f2 + 2 + -2f2

Reorder the terms:
2 + 3f + -2f2 = -2 + 2 + 2f2 + -2f2

Combine like terms: -2 + 2 = 0
2 + 3f + -2f2 = 0 + 2f2 + -2f2
2 + 3f + -2f2 = 2f2 + -2f2

Combine like terms: 2f2 + -2f2 = 0
2 + 3f + -2f2 = 0

Factor a trinomial.
(2 + -1f)(1 + 2f) = 0

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

Simplifying
2 + -1f = 0

Solving
2 + -1f = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1f = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1f = 0 + -2
-1f = 0 + -2

Combine like terms: 0 + -2 = -2
-1f = -2

Divide each side by '-1'.
f = 2

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

Simplifying
1 + 2f = 0

Solving
1 + 2f = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2f = 0 + -1
2f = 0 + -1

Combine like terms: 0 + -1 = -1
2f = -1

Divide each side by '2'.
f = -0.5

Simplifying
f = -0.5
Solution
f = {2, -0.5}