(5a+3)(2a-6)=0

Solution for (5a+3)(2a-6)=0 equation:

Simplifying
(5a + 3)(2a + -6) = 0

Reorder the terms:
(3 + 5a)(2a + -6) = 0

Reorder the terms:
(3 + 5a)(-6 + 2a) = 0

Multiply (3 + 5a) * (-6 + 2a)
(3(-6 + 2a) + 5a * (-6 + 2a)) = 0
((-6 * 3 + 2a * 3) + 5a * (-6 + 2a)) = 0
((-18 + 6a) + 5a * (-6 + 2a)) = 0
(-18 + 6a + (-6 * 5a + 2a * 5a)) = 0
(-18 + 6a + (-30a + 10a2)) = 0

Combine like terms: 6a + -30a = -24a
(-18 + -24a + 10a2) = 0

Solving
-18 + -24a + 10a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -12a + 5a2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.6, 3}