56x(x+1)+7x=45353

Solution for 56x(x+1)+7x=45353 equation:

Simplifying
56x(x + 1) + 7x = 45353

Reorder the terms:
56x(1 + x) + 7x = 45353
(1 * 56x + x * 56x) + 7x = 45353
(56x + 56x2) + 7x = 45353

Reorder the terms:
56x + 7x + 56x2 = 45353

Combine like terms: 56x + 7x = 63x
63x + 56x2 = 45353

Solving
63x + 56x2 = 45353

Solving for variable 'x'.

Reorder the terms:
-45353 + 63x + 56x2 = 45353 + -45353

Combine like terms: 45353 + -45353 = 0
-45353 + 63x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6479 + 9x + 8x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6479 + 9x + 8x2)' equal to zero and attempt to solve:

Simplifying
-6479 + 9x + 8x2 = 0

Solving
-6479 + 9x + 8x2 = 0

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

Divide each side by '8'.
-809.875 + 1.125x + x2 = 0

Move the constant term to the right:

Add '809.875' to each side of the equation.
-809.875 + 1.125x + 809.875 + x2 = 0 + 809.875

Reorder the terms:
-809.875 + 809.875 + 1.125x + x2 = 0 + 809.875

Combine like terms: -809.875 + 809.875 = 0.000
0.000 + 1.125x + x2 = 0 + 809.875
1.125x + x2 = 0 + 809.875

Combine like terms: 0 + 809.875 = 809.875
1.125x + x2 = 809.875

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 809.875 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 809.875 + 0.31640625

Combine like terms: 809.875 + 0.31640625 = 810.19140625
0.31640625 + 1.125x + x2 = 810.19140625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 810.19140625

Calculate the square root of the right side: 28.463861408

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 28.463861408 and -28.463861408.

Subproblem 1
x + 0.5625 = 28.463861408

Simplifying
x + 0.5625 = 28.463861408

Reorder the terms:
0.5625 + x = 28.463861408

Solving
0.5625 + x = 28.463861408

Solving for variable 'x'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + x = 28.463861408 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + x = 28.463861408 + -0.5625
x = 28.463861408 + -0.5625

Combine like terms: 28.463861408 + -0.5625 = 27.901361408
x = 27.901361408

Simplifying
x = 27.901361408

Subproblem 2
x + 0.5625 = -28.463861408

Simplifying
x + 0.5625 = -28.463861408

Reorder the terms:
0.5625 + x = -28.463861408

Solving
0.5625 + x = -28.463861408

Solving for variable 'x'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + x = -28.463861408 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + x = -28.463861408 + -0.5625
x = -28.463861408 + -0.5625

Combine like terms: -28.463861408 + -0.5625 = -29.026361408
x = -29.026361408

Simplifying
x = -29.026361408

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.901361408, -29.026361408}
Solution
x = {27.901361408, -29.026361408}