10g^2-3gh-h^2=0

Solution for 10g^2-3gh-h^2=0 equation:

Simplifying
10g2 + -3gh + -1h2 = 0

Reorder the terms:
-3gh + 10g2 + -1h2 = 0

Solving
-3gh + 10g2 + -1h2 = 0

Solving for variable 'g'.

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

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

Simplifying
2g + -1h = 0

Solving
2g + -1h = 0

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

Add 'h' to each side of the equation.
2g + -1h + h = 0 + h

Combine like terms: -1h + h = 0
2g + 0 = 0 + h
2g = 0 + h
Remove the zero:
2g = h

Divide each side by '2'.
g = 0.5h

Simplifying
g = 0.5h
Subproblem 2
Set the factor '(5g + h)' equal to zero and attempt to solve:

Simplifying
5g + h = 0

Solving
5g + h = 0

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

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

Combine like terms: h + -1h = 0
5g + 0 = 0 + -1h
5g = 0 + -1h
Remove the zero:
5g = -1h

Divide each side by '5'.
g = -0.2h

Simplifying
g = -0.2h
Solution
g = {0.5h, -0.2h}