8(5a+3)(a-1)=0

Solution for 8(5a+3)(a-1)=0 equation:

Simplifying
8(5a + 3)(a + -1) = 0

Reorder the terms:
8(3 + 5a)(a + -1) = 0

Reorder the terms:
8(3 + 5a)(-1 + a) = 0

Multiply (3 + 5a) * (-1 + a)
8(3(-1 + a) + 5a * (-1 + a)) = 0
8((-1 * 3 + a * 3) + 5a * (-1 + a)) = 0
8((-3 + 3a) + 5a * (-1 + a)) = 0
8(-3 + 3a + (-1 * 5a + a * 5a)) = 0
8(-3 + 3a + (-5a + 5a2)) = 0

Combine like terms: 3a + -5a = -2a
8(-3 + -2a + 5a2) = 0
(-3 * 8 + -2a * 8 + 5a2 * 8) = 0
(-24 + -16a + 40a2) = 0

Solving
-24 + -16a + 40a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + -2a + 5a2) = 0

Factor a trinomial.
8((-3 + -5a)(1 + -1a)) = 0

Ignore the factor 8.
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 '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

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

Simplifying
a = 1
Solution
a = {-0.6, 1}