x(x+4)-3=4x(x+19.5)

Solution for x(x+4)-3=4x(x+19.5) equation:

Simplifying
x(x + 4) + -3 = 4x(x + 19.5)

Reorder the terms:
x(4 + x) + -3 = 4x(x + 19.5)
(4 * x + x * x) + -3 = 4x(x + 19.5)
(4x + x2) + -3 = 4x(x + 19.5)

Reorder the terms:
-3 + 4x + x2 = 4x(x + 19.5)

Reorder the terms:
-3 + 4x + x2 = 4x(19.5 + x)
-3 + 4x + x2 = (19.5 * 4x + x * 4x)
-3 + 4x + x2 = (78x + 4x2)

Solving
-3 + 4x + x2 = 78x + 4x2

Solving for variable 'x'.

Reorder the terms:
-3 + 4x + -78x + x2 + -4x2 = 78x + 4x2 + -78x + -4x2

Combine like terms: 4x + -78x = -74x
-3 + -74x + x2 + -4x2 = 78x + 4x2 + -78x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-3 + -74x + -3x2 = 78x + 4x2 + -78x + -4x2

Reorder the terms:
-3 + -74x + -3x2 = 78x + -78x + 4x2 + -4x2

Combine like terms: 78x + -78x = 0
-3 + -74x + -3x2 = 0 + 4x2 + -4x2
-3 + -74x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + -74x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 74x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 74x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + 74x + 3x2 = 0

Solving
3 + 74x + 3x2 = 0

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

Divide each side by '3'.
1 + 24.66666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 24.66666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 24.66666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 24.66666667x + x2 = 0 + -1
24.66666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
24.66666667x + x2 = -1

The x term is 24.66666667x.  Take half its coefficient (12.33333334).
Square it (152.1111113) and add it to both sides.

Add '152.1111113' to each side of the equation.
24.66666667x + 152.1111113 + x2 = -1 + 152.1111113

Reorder the terms:
152.1111113 + 24.66666667x + x2 = -1 + 152.1111113

Combine like terms: -1 + 152.1111113 = 151.1111113
152.1111113 + 24.66666667x + x2 = 151.1111113

Factor a perfect square on the left side:
(x + 12.33333334)(x + 12.33333334) = 151.1111113

Calculate the square root of the right side: 12.292725951

Break this problem into two subproblems by setting 
(x + 12.33333334) equal to 12.292725951 and -12.292725951.

Subproblem 1
x + 12.33333334 = 12.292725951

Simplifying
x + 12.33333334 = 12.292725951

Reorder the terms:
12.33333334 + x = 12.292725951

Solving
12.33333334 + x = 12.292725951

Solving for variable 'x'.

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

Add '-12.33333334' to each side of the equation.
12.33333334 + -12.33333334 + x = 12.292725951 + -12.33333334

Combine like terms: 12.33333334 + -12.33333334 = 0.00000000
0.00000000 + x = 12.292725951 + -12.33333334
x = 12.292725951 + -12.33333334

Combine like terms: 12.292725951 + -12.33333334 = -0.040607389
x = -0.040607389

Simplifying
x = -0.040607389

Subproblem 2
x + 12.33333334 = -12.292725951

Simplifying
x + 12.33333334 = -12.292725951

Reorder the terms:
12.33333334 + x = -12.292725951

Solving
12.33333334 + x = -12.292725951

Solving for variable 'x'.

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

Add '-12.33333334' to each side of the equation.
12.33333334 + -12.33333334 + x = -12.292725951 + -12.33333334

Combine like terms: 12.33333334 + -12.33333334 = 0.00000000
0.00000000 + x = -12.292725951 + -12.33333334
x = -12.292725951 + -12.33333334

Combine like terms: -12.292725951 + -12.33333334 = -24.626059291
x = -24.626059291

Simplifying
x = -24.626059291

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.040607389, -24.626059291}
Solution
x = {-0.040607389, -24.626059291}