(x+14)(x+4)=14(x+22)

Solution for (x+14)(x+4)=14(x+22) equation:

Simplifying
(x + 14)(x + 4) = 14(x + 22)

Reorder the terms:
(14 + x)(x + 4) = 14(x + 22)

Reorder the terms:
(14 + x)(4 + x) = 14(x + 22)

Multiply (14 + x) * (4 + x)
(14(4 + x) + x(4 + x)) = 14(x + 22)
((4 * 14 + x * 14) + x(4 + x)) = 14(x + 22)
((56 + 14x) + x(4 + x)) = 14(x + 22)
(56 + 14x + (4 * x + x * x)) = 14(x + 22)
(56 + 14x + (4x + x2)) = 14(x + 22)

Combine like terms: 14x + 4x = 18x
(56 + 18x + x2) = 14(x + 22)

Reorder the terms:
56 + 18x + x2 = 14(22 + x)
56 + 18x + x2 = (22 * 14 + x * 14)
56 + 18x + x2 = (308 + 14x)

Solving
56 + 18x + x2 = 308 + 14x

Solving for variable 'x'.

Reorder the terms:
56 + -308 + 18x + -14x + x2 = 308 + 14x + -308 + -14x

Combine like terms: 56 + -308 = -252
-252 + 18x + -14x + x2 = 308 + 14x + -308 + -14x

Combine like terms: 18x + -14x = 4x
-252 + 4x + x2 = 308 + 14x + -308 + -14x

Reorder the terms:
-252 + 4x + x2 = 308 + -308 + 14x + -14x

Combine like terms: 308 + -308 = 0
-252 + 4x + x2 = 0 + 14x + -14x
-252 + 4x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-252 + 4x + x2 = 0

Factor a trinomial.
(-18 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 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 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-18, 14}