(2G+1)(G-10)=0

Solution for (2G+1)(G-10)=0 equation:

Simplifying
(2G + 1)(G + -10) = 0

Reorder the terms:
(1 + 2G)(G + -10) = 0

Reorder the terms:
(1 + 2G)(-10 + G) = 0

Multiply (1 + 2G) * (-10 + G)
(1(-10 + G) + 2G * (-10 + G)) = 0
((-10 * 1 + G * 1) + 2G * (-10 + G)) = 0
((-10 + 1G) + 2G * (-10 + G)) = 0
(-10 + 1G + (-10 * 2G + G * 2G)) = 0
(-10 + 1G + (-20G + 2G2)) = 0

Combine like terms: 1G + -20G = -19G
(-10 + -19G + 2G2) = 0

Solving
-10 + -19G + 2G2 = 0

Solving for variable 'G'.

Factor a trinomial.
(-1 + -2G)(10 + -1G) = 0

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

Simplifying
-1 + -2G = 0

Solving
-1 + -2G = 0

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

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

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

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

Divide each side by '-2'.
G = -0.5

Simplifying
G = -0.5
Subproblem 2
Set the factor '(10 + -1G)' equal to zero and attempt to solve:

Simplifying
10 + -1G = 0

Solving
10 + -1G = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1G = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1G = 0 + -10
-1G = 0 + -10

Combine like terms: 0 + -10 = -10
-1G = -10

Divide each side by '-1'.
G = 10

Simplifying
G = 10
Solution
G = {-0.5, 10}