(2x+14)(2x+20)=352

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Solution for (2x+14)(2x+20)=352 equation: 


Simplifying
(2x + 14)(2x + 20) = 352

Reorder the terms:
(14 + 2x)(2x + 20) = 352

Reorder the terms:
(14 + 2x)(20 + 2x) = 352

Multiply (14 + 2x) * (20 + 2x)
(14(20 + 2x) + 2x * (20 + 2x)) = 352
((20 * 14 + 2x * 14) + 2x * (20 + 2x)) = 352
((280 + 28x) + 2x * (20 + 2x)) = 352
(280 + 28x + (20 * 2x + 2x * 2x)) = 352
(280 + 28x + (40x + 4x2)) = 352

Combine like terms: 28x + 40x = 68x
(280 + 68x + 4x2) = 352

Solving
280 + 68x + 4x2 = 352

Solving for variable 'x'.

Reorder the terms:
280 + -352 + 68x + 4x2 = 352 + -352

Combine like terms: 280 + -352 = -72
-72 + 68x + 4x2 = 352 + -352

Combine like terms: 352 + -352 = 0
-72 + 68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 17x + x2) = 0

Factor a trinomial.
4((-18 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

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 '(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 = {-18, 1}

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