(g-7)(2g-1)=0

Solution for (g-7)(2g-1)=0 equation:

Simplifying
(g + -7)(2g + -1) = 0

Reorder the terms:
(-7 + g)(2g + -1) = 0

Reorder the terms:
(-7 + g)(-1 + 2g) = 0

Multiply (-7 + g) * (-1 + 2g)
(-7(-1 + 2g) + g(-1 + 2g)) = 0
((-1 * -7 + 2g * -7) + g(-1 + 2g)) = 0
((7 + -14g) + g(-1 + 2g)) = 0
(7 + -14g + (-1 * g + 2g * g)) = 0
(7 + -14g + (-1g + 2g2)) = 0

Combine like terms: -14g + -1g = -15g
(7 + -15g + 2g2) = 0

Solving
7 + -15g + 2g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(1 + -2g)(7 + -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 '(7 + -1g)' equal to zero and attempt to solve:

Simplifying
7 + -1g = 0

Solving
7 + -1g = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1g = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1g = 0 + -7
-1g = 0 + -7

Combine like terms: 0 + -7 = -7
-1g = -7

Divide each side by '-1'.
g = 7

Simplifying
g = 7
Solution
g = {0.5, 7}