6f^2+3-4f+5-10f^2=0

Solution for 6f^2+3-4f+5-10f^2=0 equation:

Simplifying
6f2 + 3 + -4f + 5 + -10f2 = 0

Reorder the terms:
3 + 5 + -4f + 6f2 + -10f2 = 0

Combine like terms: 3 + 5 = 8
8 + -4f + 6f2 + -10f2 = 0

Combine like terms: 6f2 + -10f2 = -4f2
8 + -4f + -4f2 = 0

Solving
8 + -4f + -4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -1f + -1f2) = 0

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

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

Simplifying
1 + -1f = 0

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

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

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

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

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