a(x+1)(x+4)=

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

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

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

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

Multiply (1 + x) * (4 + x)
a(1(4 + x) + x(4 + x)) = 0
a((4 * 1 + x * 1) + x(4 + x)) = 0
a((4 + 1x) + x(4 + x)) = 0
a(4 + 1x + (4 * x + x * x)) = 0
a(4 + 1x + (4x + x2)) = 0

Combine like terms: 1x + 4x = 5x
a(4 + 5x + x2) = 0
(4 * a + 5x * a + x2 * a) = 0
(4a + 5ax + ax2) = 0

Solving
4a + 5ax + ax2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + 5x + x2) = 0

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

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Add '-1x' to each side of the equation.
x + -1x = -4 + -1x

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

Simplifying
0 = -4 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Add '-1x' to each side of the equation.
x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
0 = -1 + -1x

Simplifying
0 = -1 + -1x

The solution to this equation could not be determined.

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