4f^2-15f+1=-13

Solution for 4f^2-15f+1=-13 equation:

Simplifying
4f2 + -15f + 1 = -13

Reorder the terms:
1 + -15f + 4f2 = -13

Solving
1 + -15f + 4f2 = -13

Solving for variable 'f'.

Reorder the terms:
1 + 13 + -15f + 4f2 = -13 + 13

Combine like terms: 1 + 13 = 14
14 + -15f + 4f2 = -13 + 13

Combine like terms: -13 + 13 = 0
14 + -15f + 4f2 = 0

Factor a trinomial.
(7 + -4f)(2 + -1f) = 0

Subproblem 1
Set the factor '(7 + -4f)' equal to zero and attempt to solve:

Simplifying
7 + -4f = 0

Solving
7 + -4f = 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 + -4f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4f = 0 + -7
-4f = 0 + -7

Combine like terms: 0 + -7 = -7
-4f = -7

Divide each side by '-4'.
f = 1.75

Simplifying
f = 1.75
Subproblem 2
Set the factor '(2 + -1f)' equal to zero and attempt to solve:

Simplifying
2 + -1f = 0

Solving
2 + -1f = 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 + -1f = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1f = 0 + -2
-1f = 0 + -2

Combine like terms: 0 + -2 = -2
-1f = -2

Divide each side by '-1'.
f = 2

Simplifying
f = 2
Solution
f = {1.75, 2}