(a+4)(7a+1)=

Solution for (a+4)(7a+1)= equation:

Simplifying
(a + 4)(7a + 1) = 0

Reorder the terms:
(4 + a)(7a + 1) = 0

Reorder the terms:
(4 + a)(1 + 7a) = 0

Multiply (4 + a) * (1 + 7a)
(4(1 + 7a) + a(1 + 7a)) = 0
((1 * 4 + 7a * 4) + a(1 + 7a)) = 0
((4 + 28a) + a(1 + 7a)) = 0
(4 + 28a + (1 * a + 7a * a)) = 0
(4 + 28a + (1a + 7a2)) = 0

Combine like terms: 28a + 1a = 29a
(4 + 29a + 7a2) = 0

Solving
4 + 29a + 7a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + a)(1 + 7a) = 0

Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

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

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

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

Simplifying
a = -4
Subproblem 2
Set the factor '(1 + 7a)' equal to zero and attempt to solve:

Simplifying
1 + 7a = 0

Solving
1 + 7a = 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 + 7a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7a = 0 + -1
7a = 0 + -1

Combine like terms: 0 + -1 = -1
7a = -1

Divide each side by '7'.
a = -0.1428571429

Simplifying
a = -0.1428571429
Solution
a = {-4, -0.1428571429}