-2f^2-f+12=-3f^2+6f

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


Simplifying
-2f2 + -1f + 12 = -3f2 + 6f

Reorder the terms:
12 + -1f + -2f2 = -3f2 + 6f

Reorder the terms:
12 + -1f + -2f2 = 6f + -3f2

Solving
12 + -1f + -2f2 = 6f + -3f2

Solving for variable 'f'.

Reorder the terms:
12 + -1f + -6f + -2f2 + 3f2 = 6f + -3f2 + -6f + 3f2

Combine like terms: -1f + -6f = -7f
12 + -7f + -2f2 + 3f2 = 6f + -3f2 + -6f + 3f2

Combine like terms: -2f2 + 3f2 = 1f2
12 + -7f + 1f2 = 6f + -3f2 + -6f + 3f2

Reorder the terms:
12 + -7f + 1f2 = 6f + -6f + -3f2 + 3f2

Combine like terms: 6f + -6f = 0
12 + -7f + 1f2 = 0 + -3f2 + 3f2
12 + -7f + 1f2 = -3f2 + 3f2

Combine like terms: -3f2 + 3f2 = 0
12 + -7f + 1f2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1f)' equal to zero and attempt to solve:

Simplifying
4 + -1f = 0

Solving
4 + -1f = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1f = 0 + -4
-1f = 0 + -4

Combine like terms: 0 + -4 = -4
-1f = -4

Divide each side by '-1'.
f = 4

Simplifying
f = 4
Solution
f = {3, 4}

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