4f^2+12f-7=0

Solution for 4f^2+12f-7=0 equation:

Simplifying
4f2 + 12f + -7 = 0

Reorder the terms:
-7 + 12f + 4f2 = 0

Solving
-7 + 12f + 4f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-7 + -2f)(1 + -2f) = 0

Subproblem 1
Set the factor '(-7 + -2f)' equal to zero and attempt to solve:

Simplifying
-7 + -2f = 0

Solving
-7 + -2f = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2f = 0 + 7

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

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

Divide each side by '-2'.
f = -3.5

Simplifying
f = -3.5
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 = {-3.5, 0.5}