(4x+16)(2x+34)=180

Solution for (4x+16)(2x+34)=180 equation:

Simplifying
(4x + 16)(2x + 34) = 180

Reorder the terms:
(16 + 4x)(2x + 34) = 180

Reorder the terms:
(16 + 4x)(34 + 2x) = 180

Multiply (16 + 4x) * (34 + 2x)
(16(34 + 2x) + 4x * (34 + 2x)) = 180
((34 * 16 + 2x * 16) + 4x * (34 + 2x)) = 180
((544 + 32x) + 4x * (34 + 2x)) = 180
(544 + 32x + (34 * 4x + 2x * 4x)) = 180
(544 + 32x + (136x + 8x2)) = 180

Combine like terms: 32x + 136x = 168x
(544 + 168x + 8x2) = 180

Solving
544 + 168x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
544 + -180 + 168x + 8x2 = 180 + -180

Combine like terms: 544 + -180 = 364
364 + 168x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
364 + 168x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(91 + 42x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(91 + 42x + 2x2)' equal to zero and attempt to solve:

Simplifying
91 + 42x + 2x2 = 0

Solving
91 + 42x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
45.5 + 21x + x2 = 0

Move the constant term to the right:

Add '-45.5' to each side of the equation.
45.5 + 21x + -45.5 + x2 = 0 + -45.5

Reorder the terms:
45.5 + -45.5 + 21x + x2 = 0 + -45.5

Combine like terms: 45.5 + -45.5 = 0.0
0.0 + 21x + x2 = 0 + -45.5
21x + x2 = 0 + -45.5

Combine like terms: 0 + -45.5 = -45.5
21x + x2 = -45.5

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -45.5 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -45.5 + 110.25

Combine like terms: -45.5 + 110.25 = 64.75
110.25 + 21x + x2 = 64.75

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 64.75

Calculate the square root of the right side: 8.04673847

Break this problem into two subproblems by setting 
(x + 10.5) equal to 8.04673847 and -8.04673847.

Subproblem 1
x + 10.5 = 8.04673847

Simplifying
x + 10.5 = 8.04673847

Reorder the terms:
10.5 + x = 8.04673847

Solving
10.5 + x = 8.04673847

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 8.04673847 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 8.04673847 + -10.5
x = 8.04673847 + -10.5

Combine like terms: 8.04673847 + -10.5 = -2.45326153
x = -2.45326153

Simplifying
x = -2.45326153

Subproblem 2
x + 10.5 = -8.04673847

Simplifying
x + 10.5 = -8.04673847

Reorder the terms:
10.5 + x = -8.04673847

Solving
10.5 + x = -8.04673847

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -8.04673847 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -8.04673847 + -10.5
x = -8.04673847 + -10.5

Combine like terms: -8.04673847 + -10.5 = -18.54673847
x = -18.54673847

Simplifying
x = -18.54673847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.45326153, -18.54673847}
Solution
x = {-2.45326153, -18.54673847}