5g(g-4)+48=2g(g+3)

Solution for 5g(g-4)+48=2g(g+3) equation:

Simplifying
5g(g + -4) + 48 = 2g(g + 3)

Reorder the terms:
5g(-4 + g) + 48 = 2g(g + 3)
(-4 * 5g + g * 5g) + 48 = 2g(g + 3)
(-20g + 5g2) + 48 = 2g(g + 3)

Reorder the terms:
48 + -20g + 5g2 = 2g(g + 3)

Reorder the terms:
48 + -20g + 5g2 = 2g(3 + g)
48 + -20g + 5g2 = (3 * 2g + g * 2g)
48 + -20g + 5g2 = (6g + 2g2)

Solving
48 + -20g + 5g2 = 6g + 2g2

Solving for variable 'g'.

Reorder the terms:
48 + -20g + -6g + 5g2 + -2g2 = 6g + 2g2 + -6g + -2g2

Combine like terms: -20g + -6g = -26g
48 + -26g + 5g2 + -2g2 = 6g + 2g2 + -6g + -2g2

Combine like terms: 5g2 + -2g2 = 3g2
48 + -26g + 3g2 = 6g + 2g2 + -6g + -2g2

Reorder the terms:
48 + -26g + 3g2 = 6g + -6g + 2g2 + -2g2

Combine like terms: 6g + -6g = 0
48 + -26g + 3g2 = 0 + 2g2 + -2g2
48 + -26g + 3g2 = 2g2 + -2g2

Combine like terms: 2g2 + -2g2 = 0
48 + -26g + 3g2 = 0

Factor a trinomial.
(8 + -3g)(6 + -1g) = 0

Subproblem 1
Set the factor '(8 + -3g)' equal to zero and attempt to solve:

Simplifying
8 + -3g = 0

Solving
8 + -3g = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3g = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3g = 0 + -8
-3g = 0 + -8

Combine like terms: 0 + -8 = -8
-3g = -8

Divide each side by '-3'.
g = 2.666666667

Simplifying
g = 2.666666667
Subproblem 2
Set the factor '(6 + -1g)' equal to zero and attempt to solve:

Simplifying
6 + -1g = 0

Solving
6 + -1g = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1g = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1g = 0 + -6
-1g = 0 + -6

Combine like terms: 0 + -6 = -6
-1g = -6

Divide each side by '-1'.
g = 6

Simplifying
g = 6
Solution
g = {2.666666667, 6}