234=(x+3)(2x+14)

Solution for 234=(x+3)(2x+14) equation:

Simplifying
234 = (x + 3)(2x + 14)

Reorder the terms:
234 = (3 + x)(2x + 14)

Reorder the terms:
234 = (3 + x)(14 + 2x)

Multiply (3 + x) * (14 + 2x)
234 = (3(14 + 2x) + x(14 + 2x))
234 = ((14 * 3 + 2x * 3) + x(14 + 2x))
234 = ((42 + 6x) + x(14 + 2x))
234 = (42 + 6x + (14 * x + 2x * x))
234 = (42 + 6x + (14x + 2x2))

Combine like terms: 6x + 14x = 20x
234 = (42 + 20x + 2x2)

Solving
234 = 42 + 20x + 2x2

Solving for variable 'x'.

Combine like terms: 234 + -42 = 192
192 + -20x + -2x2 = 42 + 20x + 2x2 + -42 + -20x + -2x2

Reorder the terms:
192 + -20x + -2x2 = 42 + -42 + 20x + -20x + 2x2 + -2x2

Combine like terms: 42 + -42 = 0
192 + -20x + -2x2 = 0 + 20x + -20x + 2x2 + -2x2
192 + -20x + -2x2 = 20x + -20x + 2x2 + -2x2

Combine like terms: 20x + -20x = 0
192 + -20x + -2x2 = 0 + 2x2 + -2x2
192 + -20x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
192 + -20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(96 + -10x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(16 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {6, -16}