f^2-4f+2=-7f

Solution for f^2-4f+2=-7f equation:

Simplifying
f2 + -4f + 2 = -7f

Reorder the terms:
2 + -4f + f2 = -7f

Solving
2 + -4f + f2 = -7f

Solving for variable 'f'.

Reorder the terms:
2 + -4f + 7f + f2 = -7f + 7f

Combine like terms: -4f + 7f = 3f
2 + 3f + f2 = -7f + 7f

Combine like terms: -7f + 7f = 0
2 + 3f + f2 = 0

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

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

Simplifying
2 + f = 0

Solving
2 + f = 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 + f = 0 + -2

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

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

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

Simplifying
1 + f = 0

Solving
1 + f = 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 + f = 0 + -1

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

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

Simplifying
f = -1
Solution
f = {-2, -1}