(x+4)(4x+2)=0

Solution for (x+4)(4x+2)=0 equation:

Simplifying
(x + 4)(4x + 2) = 0

Reorder the terms:
(4 + x)(4x + 2) = 0

Reorder the terms:
(4 + x)(2 + 4x) = 0

Multiply (4 + x) * (2 + 4x)
(4(2 + 4x) + x(2 + 4x)) = 0
((2 * 4 + 4x * 4) + x(2 + 4x)) = 0
((8 + 16x) + x(2 + 4x)) = 0
(8 + 16x + (2 * x + 4x * x)) = 0
(8 + 16x + (2x + 4x2)) = 0

Combine like terms: 16x + 2x = 18x
(8 + 18x + 4x2) = 0

Solving
8 + 18x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 9x + 2x2) = 0

Factor a trinomial.
2((4 + x)(1 + 2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x 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

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-4, -0.5}