5x(3x+7)+(4x+1)2=-19x+63

Solution for 5x(3x+7)+(4x+1)2=-19x+63 equation:

Simplifying
5x(3x + 7) + (4x + 1) * 2 = -19x + 63

Reorder the terms:
5x(7 + 3x) + (4x + 1) * 2 = -19x + 63
(7 * 5x + 3x * 5x) + (4x + 1) * 2 = -19x + 63
(35x + 15x2) + (4x + 1) * 2 = -19x + 63

Reorder the terms:
35x + 15x2 + (1 + 4x) * 2 = -19x + 63

Reorder the terms for easier multiplication:
35x + 15x2 + 2(1 + 4x) = -19x + 63
35x + 15x2 + (1 * 2 + 4x * 2) = -19x + 63
35x + 15x2 + (2 + 8x) = -19x + 63

Reorder the terms:
2 + 35x + 8x + 15x2 = -19x + 63

Combine like terms: 35x + 8x = 43x
2 + 43x + 15x2 = -19x + 63

Reorder the terms:
2 + 43x + 15x2 = 63 + -19x

Solving
2 + 43x + 15x2 = 63 + -19x

Solving for variable 'x'.

Reorder the terms:
2 + -63 + 43x + 19x + 15x2 = 63 + -19x + -63 + 19x

Combine like terms: 2 + -63 = -61
-61 + 43x + 19x + 15x2 = 63 + -19x + -63 + 19x

Combine like terms: 43x + 19x = 62x
-61 + 62x + 15x2 = 63 + -19x + -63 + 19x

Reorder the terms:
-61 + 62x + 15x2 = 63 + -63 + -19x + 19x

Combine like terms: 63 + -63 = 0
-61 + 62x + 15x2 = 0 + -19x + 19x
-61 + 62x + 15x2 = -19x + 19x

Combine like terms: -19x + 19x = 0
-61 + 62x + 15x2 = 0

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

Divide each side by '15'.
-4.066666667 + 4.133333333x + x2 = 0

Move the constant term to the right:

Add '4.066666667' to each side of the equation.
-4.066666667 + 4.133333333x + 4.066666667 + x2 = 0 + 4.066666667

Reorder the terms:
-4.066666667 + 4.066666667 + 4.133333333x + x2 = 0 + 4.066666667

Combine like terms: -4.066666667 + 4.066666667 = 0.000000000
0.000000000 + 4.133333333x + x2 = 0 + 4.066666667
4.133333333x + x2 = 0 + 4.066666667

Combine like terms: 0 + 4.066666667 = 4.066666667
4.133333333x + x2 = 4.066666667

The x term is 4.133333333x.  Take half its coefficient (2.066666667).
Square it (4.271111112) and add it to both sides.

Add '4.271111112' to each side of the equation.
4.133333333x + 4.271111112 + x2 = 4.066666667 + 4.271111112

Reorder the terms:
4.271111112 + 4.133333333x + x2 = 4.066666667 + 4.271111112

Combine like terms: 4.066666667 + 4.271111112 = 8.337777779
4.271111112 + 4.133333333x + x2 = 8.337777779

Factor a perfect square on the left side:
(x + 2.066666667)(x + 2.066666667) = 8.337777779

Calculate the square root of the right side: 2.887521044

Break this problem into two subproblems by setting 
(x + 2.066666667) equal to 2.887521044 and -2.887521044.

Subproblem 1
x + 2.066666667 = 2.887521044

Simplifying
x + 2.066666667 = 2.887521044

Reorder the terms:
2.066666667 + x = 2.887521044

Solving
2.066666667 + x = 2.887521044

Solving for variable 'x'.

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

Add '-2.066666667' to each side of the equation.
2.066666667 + -2.066666667 + x = 2.887521044 + -2.066666667

Combine like terms: 2.066666667 + -2.066666667 = 0.000000000
0.000000000 + x = 2.887521044 + -2.066666667
x = 2.887521044 + -2.066666667

Combine like terms: 2.887521044 + -2.066666667 = 0.820854377
x = 0.820854377

Simplifying
x = 0.820854377

Subproblem 2
x + 2.066666667 = -2.887521044

Simplifying
x + 2.066666667 = -2.887521044

Reorder the terms:
2.066666667 + x = -2.887521044

Solving
2.066666667 + x = -2.887521044

Solving for variable 'x'.

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

Add '-2.066666667' to each side of the equation.
2.066666667 + -2.066666667 + x = -2.887521044 + -2.066666667

Combine like terms: 2.066666667 + -2.066666667 = 0.000000000
0.000000000 + x = -2.887521044 + -2.066666667
x = -2.887521044 + -2.066666667

Combine like terms: -2.887521044 + -2.066666667 = -4.954187711
x = -4.954187711

Simplifying
x = -4.954187711

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.820854377, -4.954187711}