(4a+1)(6a+6)=

Solution for (4a+1)(6a+6)= equation:

Simplifying
(4a + 1)(6a + 6) = 0

Reorder the terms:
(1 + 4a)(6a + 6) = 0

Reorder the terms:
(1 + 4a)(6 + 6a) = 0

Multiply (1 + 4a) * (6 + 6a)
(1(6 + 6a) + 4a * (6 + 6a)) = 0
((6 * 1 + 6a * 1) + 4a * (6 + 6a)) = 0
((6 + 6a) + 4a * (6 + 6a)) = 0
(6 + 6a + (6 * 4a + 6a * 4a)) = 0
(6 + 6a + (24a + 24a2)) = 0

Combine like terms: 6a + 24a = 30a
(6 + 30a + 24a2) = 0

Solving
6 + 30a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 5a + 4a2) = 0

Factor a trinomial.
6((1 + a)(1 + 4a)) = 0

Ignore the factor 6.
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 + 4a)' equal to zero and attempt to solve:

Simplifying
1 + 4a = 0

Solving
1 + 4a = 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 + 4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4a = 0 + -1
4a = 0 + -1

Combine like terms: 0 + -1 = -1
4a = -1

Divide each side by '4'.
a = -0.25

Simplifying
a = -0.25
Solution
a = {-1, -0.25}