93=(x+19)(3x+5)

Solution for 93=(x+19)(3x+5) equation:

Simplifying
93 = (x + 19)(3x + 5)

Reorder the terms:
93 = (19 + x)(3x + 5)

Reorder the terms:
93 = (19 + x)(5 + 3x)

Multiply (19 + x) * (5 + 3x)
93 = (19(5 + 3x) + x(5 + 3x))
93 = ((5 * 19 + 3x * 19) + x(5 + 3x))
93 = ((95 + 57x) + x(5 + 3x))
93 = (95 + 57x + (5 * x + 3x * x))
93 = (95 + 57x + (5x + 3x2))

Combine like terms: 57x + 5x = 62x
93 = (95 + 62x + 3x2)

Solving
93 = 95 + 62x + 3x2

Solving for variable 'x'.

Combine like terms: 93 + -95 = -2
-2 + -62x + -3x2 = 95 + 62x + 3x2 + -95 + -62x + -3x2

Reorder the terms:
-2 + -62x + -3x2 = 95 + -95 + 62x + -62x + 3x2 + -3x2

Combine like terms: 95 + -95 = 0
-2 + -62x + -3x2 = 0 + 62x + -62x + 3x2 + -3x2
-2 + -62x + -3x2 = 62x + -62x + 3x2 + -3x2

Combine like terms: 62x + -62x = 0
-2 + -62x + -3x2 = 0 + 3x2 + -3x2
-2 + -62x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + -62x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 62x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 62x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 62x + 3x2 = 0

Solving
2 + 62x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 20.66666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 20.66666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 20.66666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 20.66666667x + x2 = 0 + -0.6666666667
20.66666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
20.66666667x + x2 = -0.6666666667

The x term is 20.66666667x.  Take half its coefficient (10.33333334).
Square it (106.7777779) and add it to both sides.

Add '106.7777779' to each side of the equation.
20.66666667x + 106.7777779 + x2 = -0.6666666667 + 106.7777779

Reorder the terms:
106.7777779 + 20.66666667x + x2 = -0.6666666667 + 106.7777779

Combine like terms: -0.6666666667 + 106.7777779 = 106.1111112333
106.7777779 + 20.66666667x + x2 = 106.1111112333

Factor a perfect square on the left side:
(x + 10.33333334)(x + 10.33333334) = 106.1111112333

Calculate the square root of the right side: 10.301024766

Break this problem into two subproblems by setting 
(x + 10.33333334) equal to 10.301024766 and -10.301024766.

Subproblem 1
x + 10.33333334 = 10.301024766

Simplifying
x + 10.33333334 = 10.301024766

Reorder the terms:
10.33333334 + x = 10.301024766

Solving
10.33333334 + x = 10.301024766

Solving for variable 'x'.

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

Add '-10.33333334' to each side of the equation.
10.33333334 + -10.33333334 + x = 10.301024766 + -10.33333334

Combine like terms: 10.33333334 + -10.33333334 = 0.00000000
0.00000000 + x = 10.301024766 + -10.33333334
x = 10.301024766 + -10.33333334

Combine like terms: 10.301024766 + -10.33333334 = -0.032308574
x = -0.032308574

Simplifying
x = -0.032308574

Subproblem 2
x + 10.33333334 = -10.301024766

Simplifying
x + 10.33333334 = -10.301024766

Reorder the terms:
10.33333334 + x = -10.301024766

Solving
10.33333334 + x = -10.301024766

Solving for variable 'x'.

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

Add '-10.33333334' to each side of the equation.
10.33333334 + -10.33333334 + x = -10.301024766 + -10.33333334

Combine like terms: 10.33333334 + -10.33333334 = 0.00000000
0.00000000 + x = -10.301024766 + -10.33333334
x = -10.301024766 + -10.33333334

Combine like terms: -10.301024766 + -10.33333334 = -20.634358106
x = -20.634358106

Simplifying
x = -20.634358106

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.032308574, -20.634358106}
Solution
x = {-0.032308574, -20.634358106}