(3a-5)(2a+8)=

Solution for (3a-5)(2a+8)= equation:

Simplifying
(3a + -5)(2a + 8) = 0

Reorder the terms:
(-5 + 3a)(2a + 8) = 0

Reorder the terms:
(-5 + 3a)(8 + 2a) = 0

Multiply (-5 + 3a) * (8 + 2a)
(-5(8 + 2a) + 3a * (8 + 2a)) = 0
((8 * -5 + 2a * -5) + 3a * (8 + 2a)) = 0
((-40 + -10a) + 3a * (8 + 2a)) = 0
(-40 + -10a + (8 * 3a + 2a * 3a)) = 0
(-40 + -10a + (24a + 6a2)) = 0

Combine like terms: -10a + 24a = 14a
(-40 + 14a + 6a2) = 0

Solving
-40 + 14a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 7a + 3a2) = 0

Factor a trinomial.
2((-4 + -1a)(5 + -3a)) = 0

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

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

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

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

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

Simplifying
a = 1.666666667
Solution
a = {-4, 1.666666667}