3c^4-9c^2=12-14c^2

Solution for 3c^4-9c^2=12-14c^2 equation:

Simplifying
3c4 + -9c2 = 12 + -14c2

Reorder the terms:
-9c2 + 3c4 = 12 + -14c2

Solving
-9c2 + 3c4 = 12 + -14c2

Solving for variable 'c'.

Reorder the terms:
-12 + -9c2 + 14c2 + 3c4 = 12 + -14c2 + -12 + 14c2

Combine like terms: -9c2 + 14c2 = 5c2
-12 + 5c2 + 3c4 = 12 + -14c2 + -12 + 14c2

Reorder the terms:
-12 + 5c2 + 3c4 = 12 + -12 + -14c2 + 14c2

Combine like terms: 12 + -12 = 0
-12 + 5c2 + 3c4 = 0 + -14c2 + 14c2
-12 + 5c2 + 3c4 = -14c2 + 14c2

Combine like terms: -14c2 + 14c2 = 0
-12 + 5c2 + 3c4 = 0

Factor a trinomial.
(-3 + -1c2)(4 + -3c2) = 0

Subproblem 1
Set the factor '(-3 + -1c2)' equal to zero and attempt to solve:

Simplifying
-3 + -1c2 = 0

Solving
-3 + -1c2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1c2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1c2 = 0 + 3
-1c2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1c2 = 3

Divide each side by '-1'.
c2 = -3

Simplifying
c2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + -3c2)' equal to zero and attempt to solve:

Simplifying
4 + -3c2 = 0

Solving
4 + -3c2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3c2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3c2 = 0 + -4
-3c2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3c2 = -4

Divide each side by '-3'.
c2 = 1.333333333

Simplifying
c2 = 1.333333333

Take the square root of each side:
c = {-1.154700538, 1.154700538}
Solution
c = {-1.154700538, 1.154700538}