(4a+1)(3a+1)=13

Solution for (4a+1)(3a+1)=13 equation:

Simplifying
(4a + 1)(3a + 1) = 13

Reorder the terms:
(1 + 4a)(3a + 1) = 13

Reorder the terms:
(1 + 4a)(1 + 3a) = 13

Multiply (1 + 4a) * (1 + 3a)
(1(1 + 3a) + 4a * (1 + 3a)) = 13
((1 * 1 + 3a * 1) + 4a * (1 + 3a)) = 13
((1 + 3a) + 4a * (1 + 3a)) = 13
(1 + 3a + (1 * 4a + 3a * 4a)) = 13
(1 + 3a + (4a + 12a2)) = 13

Combine like terms: 3a + 4a = 7a
(1 + 7a + 12a2) = 13

Solving
1 + 7a + 12a2 = 13

Solving for variable 'a'.

Reorder the terms:
1 + -13 + 7a + 12a2 = 13 + -13

Combine like terms: 1 + -13 = -12
-12 + 7a + 12a2 = 13 + -13

Combine like terms: 13 + -13 = 0
-12 + 7a + 12a2 = 0

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

Subproblem 1
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
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 = {-1.333333333, 0.75}