2a(4a+3)+2a=16

Solution for 2a(4a+3)+2a=16 equation:

Simplifying
2a(4a + 3) + 2a = 16

Reorder the terms:
2a(3 + 4a) + 2a = 16
(3 * 2a + 4a * 2a) + 2a = 16
(6a + 8a2) + 2a = 16

Reorder the terms:
6a + 2a + 8a2 = 16

Combine like terms: 6a + 2a = 8a
8a + 8a2 = 16

Solving
8a + 8a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + 8a + 8a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 8a + 8a2 = 0

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

Factor a trinomial.
8((-2 + -1a)(1 + -1a)) = 0

Ignore the factor 8.
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 '(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 = {-2, 1}