f^2+3f-12=6

Solution for f^2+3f-12=6 equation:

Simplifying
f2 + 3f + -12 = 6

Reorder the terms:
-12 + 3f + f2 = 6

Solving
-12 + 3f + f2 = 6

Solving for variable 'f'.

Reorder the terms:
-12 + -6 + 3f + f2 = 6 + -6

Combine like terms: -12 + -6 = -18
-18 + 3f + f2 = 6 + -6

Combine like terms: 6 + -6 = 0
-18 + 3f + f2 = 0

Factor a trinomial.
(-6 + -1f)(3 + -1f) = 0

Subproblem 1
Set the factor '(-6 + -1f)' equal to zero and attempt to solve:

Simplifying
-6 + -1f = 0

Solving
-6 + -1f = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1f = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1f = 0 + 6
-1f = 0 + 6

Combine like terms: 0 + 6 = 6
-1f = 6

Divide each side by '-1'.
f = -6

Simplifying
f = -6
Subproblem 2
Set the factor '(3 + -1f)' equal to zero and attempt to solve:

Simplifying
3 + -1f = 0

Solving
3 + -1f = 0

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

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

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

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

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

Simplifying
f = 3
Solution
f = {-6, 3}