3(a-5)(a+2)=0

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

Simplifying
3(a + -5)(a + 2) = 0

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

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

Multiply (-5 + a) * (2 + a)
3(-5(2 + a) + a(2 + a)) = 0
3((2 * -5 + a * -5) + a(2 + a)) = 0
3((-10 + -5a) + a(2 + a)) = 0
3(-10 + -5a + (2 * a + a * a)) = 0
3(-10 + -5a + (2a + a2)) = 0

Combine like terms: -5a + 2a = -3a
3(-10 + -3a + a2) = 0
(-10 * 3 + -3a * 3 + a2 * 3) = 0
(-30 + -9a + 3a2) = 0

Solving
-30 + -9a + 3a2 = 0

Solving for variable 'a'.

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

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

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

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

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

Simplifying
a = -2
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-2, 5}