(x+3)(x+14)=0

Solution for (x+3)(x+14)=0 equation:

Simplifying
(x + 3)(x + 14) = 0

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

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

Multiply (3 + x) * (14 + x)
(3(14 + x) + x(14 + x)) = 0
((14 * 3 + x * 3) + x(14 + x)) = 0
((42 + 3x) + x(14 + x)) = 0
(42 + 3x + (14 * x + x * x)) = 0
(42 + 3x + (14x + x2)) = 0

Combine like terms: 3x + 14x = 17x
(42 + 17x + x2) = 0

Solving
42 + 17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(14 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-14, -3}