2a(a+5)(a+7)+4a=

Solution for 2a(a+5)(a+7)+4a= equation:

Simplifying
2a(a + 5)(a + 7) + 4a = 0

Reorder the terms:
2a(5 + a)(a + 7) + 4a = 0

Reorder the terms:
2a(5 + a)(7 + a) + 4a = 0

Multiply (5 + a) * (7 + a)
2a(5(7 + a) + a(7 + a)) + 4a = 0
2a((7 * 5 + a * 5) + a(7 + a)) + 4a = 0
2a((35 + 5a) + a(7 + a)) + 4a = 0
2a(35 + 5a + (7 * a + a * a)) + 4a = 0
2a(35 + 5a + (7a + a2)) + 4a = 0

Combine like terms: 5a + 7a = 12a
2a(35 + 12a + a2) + 4a = 0
(35 * 2a + 12a * 2a + a2 * 2a) + 4a = 0
(70a + 24a2 + 2a3) + 4a = 0

Reorder the terms:
70a + 4a + 24a2 + 2a3 = 0

Combine like terms: 70a + 4a = 74a
74a + 24a2 + 2a3 = 0

Solving
74a + 24a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(37 + 12a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(37 + 12a + a2)' equal to zero and attempt to solve:

Simplifying
37 + 12a + a2 = 0

Solving
37 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 12a + -37 + a2 = 0 + -37

Reorder the terms:
37 + -37 + 12a + a2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 12a + a2 = 0 + -37
12a + a2 = 0 + -37

Combine like terms: 0 + -37 = -37
12a + a2 = -37

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = -37 + 36

Reorder the terms:
36 + 12a + a2 = -37 + 36

Combine like terms: -37 + 36 = -1
36 + 12a + a2 = -1

Factor a perfect square on the left side:
(a + 6)(a + 6) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}