9900(x+5)+9900x=99x*99(x+5)

Solution for 9900(x+5)+9900x=99x*99(x+5) equation:

Simplifying
9900(x + 5) + 9900x = 99x * 99(x + 5)

Reorder the terms:
9900(5 + x) + 9900x = 99x * 99(x + 5)
(5 * 9900 + x * 9900) + 9900x = 99x * 99(x + 5)
(49500 + 9900x) + 9900x = 99x * 99(x + 5)

Combine like terms: 9900x + 9900x = 19800x
49500 + 19800x = 99x * 99(x + 5)

Reorder the terms:
49500 + 19800x = 99x * 99(5 + x)

Reorder the terms for easier multiplication:
49500 + 19800x = 99 * 99x(5 + x)

Multiply 99 * 99
49500 + 19800x = 9801x(5 + x)
49500 + 19800x = (5 * 9801x + x * 9801x)
49500 + 19800x = (49005x + 9801x2)

Solving
49500 + 19800x = 49005x + 9801x2

Solving for variable 'x'.

Combine like terms: 19800x + -49005x = -29205x
49500 + -29205x + -9801x2 = 49005x + 9801x2 + -49005x + -9801x2

Reorder the terms:
49500 + -29205x + -9801x2 = 49005x + -49005x + 9801x2 + -9801x2

Combine like terms: 49005x + -49005x = 0
49500 + -29205x + -9801x2 = 0 + 9801x2 + -9801x2
49500 + -29205x + -9801x2 = 9801x2 + -9801x2

Combine like terms: 9801x2 + -9801x2 = 0
49500 + -29205x + -9801x2 = 0

Factor out the Greatest Common Factor (GCF), '99'.
99(500 + -295x + -99x2) = 0

Ignore the factor 99.
Subproblem 1
Set the factor '(500 + -295x + -99x2)' equal to zero and attempt to solve:

Simplifying
500 + -295x + -99x2 = 0

Solving
500 + -295x + -99x2 = 0

Begin completing the square.  Divide all terms by
-99 the coefficient of the squared term: 

Divide each side by '-99'.
-5.050505051 + 2.97979798x + x2 = 0

Move the constant term to the right:

Add '5.050505051' to each side of the equation.
-5.050505051 + 2.97979798x + 5.050505051 + x2 = 0 + 5.050505051

Reorder the terms:
-5.050505051 + 5.050505051 + 2.97979798x + x2 = 0 + 5.050505051

Combine like terms: -5.050505051 + 5.050505051 = 0.000000000
0.000000000 + 2.97979798x + x2 = 0 + 5.050505051
2.97979798x + x2 = 0 + 5.050505051

Combine like terms: 0 + 5.050505051 = 5.050505051
2.97979798x + x2 = 5.050505051

The x term is 2.97979798x.  Take half its coefficient (1.48989899).
Square it (2.219799000) and add it to both sides.

Add '2.219799000' to each side of the equation.
2.97979798x + 2.219799000 + x2 = 5.050505051 + 2.219799000

Reorder the terms:
2.219799000 + 2.97979798x + x2 = 5.050505051 + 2.219799000

Combine like terms: 5.050505051 + 2.219799000 = 7.270304051
2.219799000 + 2.97979798x + x2 = 7.270304051

Factor a perfect square on the left side:
(x + 1.48989899)(x + 1.48989899) = 7.270304051

Calculate the square root of the right side: 2.696350135

Break this problem into two subproblems by setting 
(x + 1.48989899) equal to 2.696350135 and -2.696350135.

Subproblem 1
x + 1.48989899 = 2.696350135

Simplifying
x + 1.48989899 = 2.696350135

Reorder the terms:
1.48989899 + x = 2.696350135

Solving
1.48989899 + x = 2.696350135

Solving for variable 'x'.

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

Add '-1.48989899' to each side of the equation.
1.48989899 + -1.48989899 + x = 2.696350135 + -1.48989899

Combine like terms: 1.48989899 + -1.48989899 = 0.00000000
0.00000000 + x = 2.696350135 + -1.48989899
x = 2.696350135 + -1.48989899

Combine like terms: 2.696350135 + -1.48989899 = 1.206451145
x = 1.206451145

Simplifying
x = 1.206451145

Subproblem 2
x + 1.48989899 = -2.696350135

Simplifying
x + 1.48989899 = -2.696350135

Reorder the terms:
1.48989899 + x = -2.696350135

Solving
1.48989899 + x = -2.696350135

Solving for variable 'x'.

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

Add '-1.48989899' to each side of the equation.
1.48989899 + -1.48989899 + x = -2.696350135 + -1.48989899

Combine like terms: 1.48989899 + -1.48989899 = 0.00000000
0.00000000 + x = -2.696350135 + -1.48989899
x = -2.696350135 + -1.48989899

Combine like terms: -2.696350135 + -1.48989899 = -4.186249125
x = -4.186249125

Simplifying
x = -4.186249125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.206451145, -4.186249125}
Solution
x = {1.206451145, -4.186249125}