(3g+1)(2g-5)=0

Solution for (3g+1)(2g-5)=0 equation:

Simplifying
(3g + 1)(2g + -5) = 0

Reorder the terms:
(1 + 3g)(2g + -5) = 0

Reorder the terms:
(1 + 3g)(-5 + 2g) = 0

Multiply (1 + 3g) * (-5 + 2g)
(1(-5 + 2g) + 3g * (-5 + 2g)) = 0
((-5 * 1 + 2g * 1) + 3g * (-5 + 2g)) = 0
((-5 + 2g) + 3g * (-5 + 2g)) = 0
(-5 + 2g + (-5 * 3g + 2g * 3g)) = 0
(-5 + 2g + (-15g + 6g2)) = 0

Combine like terms: 2g + -15g = -13g
(-5 + -13g + 6g2) = 0

Solving
-5 + -13g + 6g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-1 + -3g)(5 + -2g) = 0

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

Simplifying
-1 + -3g = 0

Solving
-1 + -3g = 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 + -3g = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3g = 0 + 1
-3g = 0 + 1

Combine like terms: 0 + 1 = 1
-3g = 1

Divide each side by '-3'.
g = -0.3333333333

Simplifying
g = -0.3333333333
Subproblem 2
Set the factor '(5 + -2g)' equal to zero and attempt to solve:

Simplifying
5 + -2g = 0

Solving
5 + -2g = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2g = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2g = 0 + -5
-2g = 0 + -5

Combine like terms: 0 + -5 = -5
-2g = -5

Divide each side by '-2'.
g = 2.5

Simplifying
g = 2.5
Solution
g = {-0.3333333333, 2.5}