(6a+1)(a+1)=21

Solution for (6a+1)(a+1)=21 equation:

Simplifying
(6a + 1)(a + 1) = 21

Reorder the terms:
(1 + 6a)(a + 1) = 21

Reorder the terms:
(1 + 6a)(1 + a) = 21

Multiply (1 + 6a) * (1 + a)
(1(1 + a) + 6a * (1 + a)) = 21
((1 * 1 + a * 1) + 6a * (1 + a)) = 21
((1 + 1a) + 6a * (1 + a)) = 21
(1 + 1a + (1 * 6a + a * 6a)) = 21
(1 + 1a + (6a + 6a2)) = 21

Combine like terms: 1a + 6a = 7a
(1 + 7a + 6a2) = 21

Solving
1 + 7a + 6a2 = 21

Solving for variable 'a'.

Reorder the terms:
1 + -21 + 7a + 6a2 = 21 + -21

Combine like terms: 1 + -21 = -20
-20 + 7a + 6a2 = 21 + -21

Combine like terms: 21 + -21 = 0
-20 + 7a + 6a2 = 0

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

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

Simplifying
-5 + -2a = 0

Solving
-5 + -2a = 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 + -2a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5

Combine like terms: 0 + 5 = 5
-2a = 5

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:

Simplifying
4 + -3a = 0

Solving
4 + -3a = 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 + -3a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4

Combine like terms: 0 + -4 = -4
-3a = -4

Divide each side by '-3'.
a = 1.333333333

Simplifying
a = 1.333333333
Solution
a = {-2.5, 1.333333333}