4f^2+18f=10

Solution for 4f^2+18f=10 equation:

Simplifying
4f2 + 18f = 10

Reorder the terms:
18f + 4f2 = 10

Solving
18f + 4f2 = 10

Solving for variable 'f'.

Reorder the terms:
-10 + 18f + 4f2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 18f + 4f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9f + 2f2) = 0

Factor a trinomial.
2((-5 + -1f)(1 + -2f)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1f)' equal to zero and attempt to solve:

Simplifying
-5 + -1f = 0

Solving
-5 + -1f = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1f = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1f = 0 + 5
-1f = 0 + 5

Combine like terms: 0 + 5 = 5
-1f = 5

Divide each side by '-1'.
f = -5

Simplifying
f = -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 = {-5, 0.5}