(3a+10)(3a-12)=0

Solution for (3a+10)(3a-12)=0 equation:

Simplifying
(3a + 10)(3a + -12) = 0

Reorder the terms:
(10 + 3a)(3a + -12) = 0

Reorder the terms:
(10 + 3a)(-12 + 3a) = 0

Multiply (10 + 3a) * (-12 + 3a)
(10(-12 + 3a) + 3a * (-12 + 3a)) = 0
((-12 * 10 + 3a * 10) + 3a * (-12 + 3a)) = 0
((-120 + 30a) + 3a * (-12 + 3a)) = 0
(-120 + 30a + (-12 * 3a + 3a * 3a)) = 0
(-120 + 30a + (-36a + 9a2)) = 0

Combine like terms: 30a + -36a = -6a
(-120 + -6a + 9a2) = 0

Solving
-120 + -6a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + -2a + 3a2) = 0

Factor a trinomial.
3((-10 + -3a)(4 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -3a)' equal to zero and attempt to solve:

Simplifying
-10 + -3a = 0

Solving
-10 + -3a = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3a = 0 + 10
-3a = 0 + 10

Combine like terms: 0 + 10 = 10
-3a = 10

Divide each side by '-3'.
a = -3.333333333

Simplifying
a = -3.333333333
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-3.333333333, 4}