(a+1)(a*2+3a+1)=

Solution for (a+1)(a*2+3a+1)= equation:

Simplifying
(a + 1)(a * 2 + 3a + 1) = 0

Reorder the terms:
(1 + a)(a * 2 + 3a + 1) = 0

Reorder the terms for easier multiplication:
(1 + a)(2a + 3a + 1) = 0

Reorder the terms:
(1 + a)(1 + 2a + 3a) = 0

Combine like terms: 2a + 3a = 5a
(1 + a)(1 + 5a) = 0

Multiply (1 + a) * (1 + 5a)
(1(1 + 5a) + a(1 + 5a)) = 0
((1 * 1 + 5a * 1) + a(1 + 5a)) = 0
((1 + 5a) + a(1 + 5a)) = 0
(1 + 5a + (1 * a + 5a * a)) = 0
(1 + 5a + (1a + 5a2)) = 0

Combine like terms: 5a + 1a = 6a
(1 + 6a + 5a2) = 0

Solving
1 + 6a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + a)(1 + 5a) = 0

Subproblem 1
Set the factor '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
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 = {-1, -0.2}