47x+44x(33x+1)+90+111=360

Solution for 47x+44x(33x+1)+90+111=360 equation:

Simplifying
47x + 44x(33x + 1) + 90 + 111 = 360

Reorder the terms:
47x + 44x(1 + 33x) + 90 + 111 = 360
47x + (1 * 44x + 33x * 44x) + 90 + 111 = 360
47x + (44x + 1452x2) + 90 + 111 = 360

Reorder the terms:
90 + 111 + 47x + 44x + 1452x2 = 360

Combine like terms: 90 + 111 = 201
201 + 47x + 44x + 1452x2 = 360

Combine like terms: 47x + 44x = 91x
201 + 91x + 1452x2 = 360

Solving
201 + 91x + 1452x2 = 360

Solving for variable 'x'.

Reorder the terms:
201 + -360 + 91x + 1452x2 = 360 + -360

Combine like terms: 201 + -360 = -159
-159 + 91x + 1452x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-159 + 91x + 1452x2 = 0

Begin completing the square.  Divide all terms by
1452 the coefficient of the squared term: 

Divide each side by '1452'.
-0.1095041322 + 0.06267217631x + x2 = 0

Move the constant term to the right:

Add '0.1095041322' to each side of the equation.
-0.1095041322 + 0.06267217631x + 0.1095041322 + x2 = 0 + 0.1095041322

Reorder the terms:
-0.1095041322 + 0.1095041322 + 0.06267217631x + x2 = 0 + 0.1095041322

Combine like terms: -0.1095041322 + 0.1095041322 = 0.0000000000
0.0000000000 + 0.06267217631x + x2 = 0 + 0.1095041322
0.06267217631x + x2 = 0 + 0.1095041322

Combine like terms: 0 + 0.1095041322 = 0.1095041322
0.06267217631x + x2 = 0.1095041322

The x term is 0.06267217631x.  Take half its coefficient (0.03133608816).
Square it (0.0009819504212) and add it to both sides.

Add '0.0009819504212' to each side of the equation.
0.06267217631x + 0.0009819504212 + x2 = 0.1095041322 + 0.0009819504212

Reorder the terms:
0.0009819504212 + 0.06267217631x + x2 = 0.1095041322 + 0.0009819504212

Combine like terms: 0.1095041322 + 0.0009819504212 = 0.1104860826212
0.0009819504212 + 0.06267217631x + x2 = 0.1104860826212

Factor a perfect square on the left side:
(x + 0.03133608816)(x + 0.03133608816) = 0.1104860826212

Calculate the square root of the right side: 0.332394468

Break this problem into two subproblems by setting 
(x + 0.03133608816) equal to 0.332394468 and -0.332394468.

Subproblem 1
x + 0.03133608816 = 0.332394468

Simplifying
x + 0.03133608816 = 0.332394468

Reorder the terms:
0.03133608816 + x = 0.332394468

Solving
0.03133608816 + x = 0.332394468

Solving for variable 'x'.

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

Add '-0.03133608816' to each side of the equation.
0.03133608816 + -0.03133608816 + x = 0.332394468 + -0.03133608816

Combine like terms: 0.03133608816 + -0.03133608816 = 0.00000000000
0.00000000000 + x = 0.332394468 + -0.03133608816
x = 0.332394468 + -0.03133608816

Combine like terms: 0.332394468 + -0.03133608816 = 0.30105837984
x = 0.30105837984

Simplifying
x = 0.30105837984

Subproblem 2
x + 0.03133608816 = -0.332394468

Simplifying
x + 0.03133608816 = -0.332394468

Reorder the terms:
0.03133608816 + x = -0.332394468

Solving
0.03133608816 + x = -0.332394468

Solving for variable 'x'.

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

Add '-0.03133608816' to each side of the equation.
0.03133608816 + -0.03133608816 + x = -0.332394468 + -0.03133608816

Combine like terms: 0.03133608816 + -0.03133608816 = 0.00000000000
0.00000000000 + x = -0.332394468 + -0.03133608816
x = -0.332394468 + -0.03133608816

Combine like terms: -0.332394468 + -0.03133608816 = -0.36373055616
x = -0.36373055616

Simplifying
x = -0.36373055616

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.30105837984, -0.36373055616}