(g-4)(2g+1)=0

Solution for (g-4)(2g+1)=0 equation:

Simplifying
(g + -4)(2g + 1) = 0

Reorder the terms:
(-4 + g)(2g + 1) = 0

Reorder the terms:
(-4 + g)(1 + 2g) = 0

Multiply (-4 + g) * (1 + 2g)
(-4(1 + 2g) + g(1 + 2g)) = 0
((1 * -4 + 2g * -4) + g(1 + 2g)) = 0
((-4 + -8g) + g(1 + 2g)) = 0
(-4 + -8g + (1 * g + 2g * g)) = 0
(-4 + -8g + (1g + 2g2)) = 0

Combine like terms: -8g + 1g = -7g
(-4 + -7g + 2g2) = 0

Solving
-4 + -7g + 2g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-1 + -2g)(4 + -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 '(4 + -1g)' equal to zero and attempt to solve:

Simplifying
4 + -1g = 0

Solving
4 + -1g = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1g = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1g = 0 + -4
-1g = 0 + -4

Combine like terms: 0 + -4 = -4
-1g = -4

Divide each side by '-1'.
g = 4

Simplifying
g = 4
Solution
g = {-0.5, 4}