2x(6+x)=14

Solution for 2x(6+x)=14 equation:

Simplifying
2x(6 + x) = 14
(6 * 2x + x * 2x) = 14
(12x + 2x2) = 14

Solving
12x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 12x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-7, 1}