(x+4)(x+14)=0

Solution for (x+4)(x+14)=0 equation:

Simplifying
(x + 4)(x + 14) = 0

Reorder the terms:
(4 + x)(x + 14) = 0

Reorder the terms:
(4 + x)(14 + x) = 0

Multiply (4 + x) * (14 + x)
(4(14 + x) + x(14 + x)) = 0
((14 * 4 + x * 4) + x(14 + x)) = 0
((56 + 4x) + x(14 + x)) = 0
(56 + 4x + (14 * x + x * x)) = 0
(56 + 4x + (14x + x2)) = 0

Combine like terms: 4x + 14x = 18x
(56 + 18x + x2) = 0

Solving
56 + 18x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
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 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
Solution
x = {-14, -4}