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

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

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

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

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

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

Combine like terms: 1g + 8g = 9g
(4 + 9g + 2g2) = 0

Solving
4 + 9g + 2g2 = 0

Solving for variable 'g'.

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

Subproblem 1
Set the factor '(4 + g)' equal to zero and attempt to solve:

Simplifying
4 + g = 0

Solving
4 + g = 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 + g = 0 + -4

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

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

Simplifying
g = -4
Subproblem 2
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
Solution
g = {-4, -0.5}