(5a-1)(6a+3)=

Solution for (5a-1)(6a+3)= equation:

Simplifying
(5a + -1)(6a + 3) = 0

Reorder the terms:
(-1 + 5a)(6a + 3) = 0

Reorder the terms:
(-1 + 5a)(3 + 6a) = 0

Multiply (-1 + 5a) * (3 + 6a)
(-1(3 + 6a) + 5a * (3 + 6a)) = 0
((3 * -1 + 6a * -1) + 5a * (3 + 6a)) = 0
((-3 + -6a) + 5a * (3 + 6a)) = 0
(-3 + -6a + (3 * 5a + 6a * 5a)) = 0
(-3 + -6a + (15a + 30a2)) = 0

Combine like terms: -6a + 15a = 9a
(-3 + 9a + 30a2) = 0

Solving
-3 + 9a + 30a2 = 0

Solving for variable 'a'.

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

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

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

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

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

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve:

Simplifying
1 + -5a = 0

Solving
1 + -5a = 0

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

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

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

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

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
Solution
a = {-0.5, 0.2}