2(4a+3)(a+1)=21

Solution for 2(4a+3)(a+1)=21 equation:

Simplifying
2(4a + 3)(a + 1) = 21

Reorder the terms:
2(3 + 4a)(a + 1) = 21

Reorder the terms:
2(3 + 4a)(1 + a) = 21

Multiply (3 + 4a) * (1 + a)
2(3(1 + a) + 4a * (1 + a)) = 21
2((1 * 3 + a * 3) + 4a * (1 + a)) = 21
2((3 + 3a) + 4a * (1 + a)) = 21
2(3 + 3a + (1 * 4a + a * 4a)) = 21
2(3 + 3a + (4a + 4a2)) = 21

Combine like terms: 3a + 4a = 7a
2(3 + 7a + 4a2) = 21
(3 * 2 + 7a * 2 + 4a2 * 2) = 21
(6 + 14a + 8a2) = 21

Solving
6 + 14a + 8a2 = 21

Solving for variable 'a'.

Reorder the terms:
6 + -21 + 14a + 8a2 = 21 + -21

Combine like terms: 6 + -21 = -15
-15 + 14a + 8a2 = 21 + -21

Combine like terms: 21 + -21 = 0
-15 + 14a + 8a2 = 0

Factor a trinomial.
(-5 + -2a)(3 + -4a) = 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 '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

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

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

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

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-2.5, 0.75}