(3a-6g)(3a+5g)=0

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Solution for (3a-6g)(3a+5g)=0 equation: 


Simplifying
(3a + -6g)(3a + 5g) = 0

Multiply (3a + -6g) * (3a + 5g)
(3a * (3a + 5g) + -6g * (3a + 5g)) = 0
((3a * 3a + 5g * 3a) + -6g * (3a + 5g)) = 0

Reorder the terms:
((15ag + 9a2) + -6g * (3a + 5g)) = 0
((15ag + 9a2) + -6g * (3a + 5g)) = 0
(15ag + 9a2 + (3a * -6g + 5g * -6g)) = 0
(15ag + 9a2 + (-18ag + -30g2)) = 0

Reorder the terms:
(15ag + -18ag + 9a2 + -30g2) = 0

Combine like terms: 15ag + -18ag = -3ag
(-3ag + 9a2 + -30g2) = 0

Solving
-3ag + 9a2 + -30g2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1ag + 3a2 + -10g2) = 0

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

Ignore the factor 3.

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

Simplifying
a + -2g = 0

Solving
a + -2g = 0

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

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

Combine like terms: -2g + 2g = 0
a + 0 = 0 + 2g
a = 0 + 2g
Remove the zero:
a = 2g

Simplifying
a = 2g

Subproblem 2
Set the factor '(3a + 5g)' equal to zero and attempt to solve:

Simplifying
3a + 5g = 0

Solving
3a + 5g = 0

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

Add '-5g' to each side of the equation.
3a + 5g + -5g = 0 + -5g

Combine like terms: 5g + -5g = 0
3a + 0 = 0 + -5g
3a = 0 + -5g
Remove the zero:
3a = -5g

Divide each side by '3'.
a = -1.666666667g

Simplifying
a = -1.666666667g
Solution
a = {2g, -1.666666667g}

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