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((-1 + -2f)(5 + -1f)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
f = {-0.5, 5}