2(g^2-7g+10)=0

Solution for 2(g^2-7g+10)=0 equation:

Simplifying
2(g2 + -7g + 10) = 0

Reorder the terms:
2(10 + -7g + g2) = 0
(10 * 2 + -7g * 2 + g2 * 2) = 0
(20 + -14g + 2g2) = 0

Solving
20 + -14g + 2g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7g + g2) = 0

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

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

Simplifying
2 + -1g = 0

Solving
2 + -1g = 0

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

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

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

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

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

Simplifying
g = 2
Subproblem 2
Set the factor '(5 + -1g)' equal to zero and attempt to solve:

Simplifying
5 + -1g = 0

Solving
5 + -1g = 0

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

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

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

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

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

Simplifying
g = 5
Solution
g = {2, 5}