3(x+5)=x^2-4

Solution for 3(x+5)=x^2-4 equation:

Simplifying
3(x + 5) = x2 + -4

Reorder the terms:
3(5 + x) = x2 + -4
(5 * 3 + x * 3) = x2 + -4
(15 + 3x) = x2 + -4

Reorder the terms:
15 + 3x = -4 + x2

Solving
15 + 3x = -4 + x2

Solving for variable 'x'.

Reorder the terms:
15 + 4 + 3x + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: 15 + 4 = 19
19 + 3x + -1x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
19 + 3x + -1x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
19 + 3x + -1x2 = 0 + x2 + -1x2
19 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
19 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + -3x + x2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -3x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -3x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3x + x2 = 0 + 19
-3x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-3x + x2 = 19

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 19 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + -3x + x2 = 21.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
x + -1.5 = 4.609772229

Simplifying
x + -1.5 = 4.609772229

Reorder the terms:
-1.5 + x = 4.609772229

Solving
-1.5 + x = 4.609772229

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.609772229 + 1.5
x = 4.609772229 + 1.5

Combine like terms: 4.609772229 + 1.5 = 6.109772229
x = 6.109772229

Simplifying
x = 6.109772229

Subproblem 2
x + -1.5 = -4.609772229

Simplifying
x + -1.5 = -4.609772229

Reorder the terms:
-1.5 + x = -4.609772229

Solving
-1.5 + x = -4.609772229

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.609772229 + 1.5
x = -4.609772229 + 1.5

Combine like terms: -4.609772229 + 1.5 = -3.109772229
x = -3.109772229

Simplifying
x = -3.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.109772229, -3.109772229}