(4g+1)(3g-6)=0

Solution for (4g+1)(3g-6)=0 equation:

Simplifying
(4g + 1)(3g + -6) = 0

Reorder the terms:
(1 + 4g)(3g + -6) = 0

Reorder the terms:
(1 + 4g)(-6 + 3g) = 0

Multiply (1 + 4g) * (-6 + 3g)
(1(-6 + 3g) + 4g * (-6 + 3g)) = 0
((-6 * 1 + 3g * 1) + 4g * (-6 + 3g)) = 0
((-6 + 3g) + 4g * (-6 + 3g)) = 0
(-6 + 3g + (-6 * 4g + 3g * 4g)) = 0
(-6 + 3g + (-24g + 12g2)) = 0

Combine like terms: 3g + -24g = -21g
(-6 + -21g + 12g2) = 0

Solving
-6 + -21g + 12g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -7g + 4g2) = 0

Factor a trinomial.
3((-1 + -4g)(2 + -1g)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -4g)' equal to zero and attempt to solve:

Simplifying
-1 + -4g = 0

Solving
-1 + -4g = 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 + -4g = 0 + 1

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

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

Divide each side by '-4'.
g = -0.25

Simplifying
g = -0.25
Subproblem 2
Set the factor '(2 + -1g)' equal to zero and attempt to solve:

Simplifying
2 + -1g = 0

Solving
2 + -1g = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1g = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g = 0 + -2
-1g = 0 + -2

Combine like terms: 0 + -2 = -2
-1g = -2

Divide each side by '-1'.
g = 2

Simplifying
g = 2
Solution
g = {-0.25, 2}