189-29x-49(41-x)(24)(21)(90)=9(x-21)(696-141)(401)(41)(62x)(41)(51)(13)

Solution for 189-29x-49(41-x)(24)(21)(90)=9(x-21)(696-141)(401)(41)(62x)(41)(51)(13) equation:

Simplifying
189 + -29x + -49(41 + -1x)(24)(21)(90) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Reorder the terms for easier multiplication:
189 + -29x + -49 * 24 * 21 * 90(41 + -1x) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Multiply -49 * 24
189 + -29x + -1176 * 21 * 90(41 + -1x) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Multiply -1176 * 21
189 + -29x + -24696 * 90(41 + -1x) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Multiply -24696 * 90
189 + -29x + -2222640(41 + -1x) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)
189 + -29x + (41 * -2222640 + -1x * -2222640) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)
189 + -29x + (-91128240 + 2222640x) = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Reorder the terms:
189 + -91128240 + -29x + 2222640x = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Combine like terms: 189 + -91128240 = -91128051
-91128051 + -29x + 2222640x = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Combine like terms: -29x + 2222640x = 2222611x
-91128051 + 2222611x = 9(x + -21)(696 + -141)(401)(41)(62x)(41)(51)(13)

Reorder the terms:
-91128051 + 2222611x = 9(-21 + x)(696 + -141)(401)(41)(62x)(41)(51)(13)

Combine like terms: 696 + -141 = 555
-91128051 + 2222611x = 9(-21 + x)(555)(401)(41)(62x)(41)(51)(13)

Remove parenthesis around (62x)
-91128051 + 2222611x = 9(-21 + x) * 555 * 401 * 41 * 62x(41)(51)(13)

Reorder the terms for easier multiplication:
-91128051 + 2222611x = 9 * 555 * 401 * 41 * 62 * 41 * 51 * 13x(-21 + x)

Multiply 9 * 555
-91128051 + 2222611x = 4995 * 401 * 41 * 62 * 41 * 51 * 13x(-21 + x)

Multiply 4995 * 401
-91128051 + 2222611x = 2002995 * 41 * 62 * 41 * 51 * 13x(-21 + x)

Multiply 2002995 * 41
-91128051 + 2222611x = 82122795 * 62 * 41 * 51 * 13x(-21 + x)

Multiply 82122795 * 62
-91128051 + 2222611x = 5091613290 * 41 * 51 * 13x(-21 + x)

Multiply 5091613290 * 41
-91128051 + 2222611x = 208756144900 * 51 * 13x(-21 + x)

Multiply 208756144900 * 51
-91128051 + 2222611x = 10646563390000 * 13x(-21 + x)

Multiply 10646563390000 * 13
-91128051 + 2222611x = 138405324100000x(-21 + x)
-91128051 + 2222611x = (-21 * 138405324100000x + x * 138405324100000x)
-91128051 + 2222611x = (-2906511806000000x + 138405324100000x2)

Solving
-91128051 + 2222611x = -2906511806000000x + 138405324100000x2

Solving for variable 'x'.

Combine like terms: 2222611x + 2906511806000000x = 2906511808222611x
-91128051 + 2906511808222611x + -138405324100000x2 = -2906511806000000x + 138405324100000x2 + 2906511806000000x + -138405324100000x2

Reorder the terms:
-91128051 + 2906511808222611x + -138405324100000x2 = -2906511806000000x + 2906511806000000x + 138405324100000x2 + -138405324100000x2

Combine like terms: -2906511806000000x + 2906511806000000x = 0
-91128051 + 2906511808222611x + -138405324100000x2 = 0 + 138405324100000x2 + -138405324100000x2
-91128051 + 2906511808222611x + -138405324100000x2 = 138405324100000x2 + -138405324100000x2

Combine like terms: 138405324100000x2 + -138405324100000x2 = 0
-91128051 + 2906511808222611x + -138405324100000x2 = 0

Begin completing the square.  Divide all terms by
-138405324100000 the coefficient of the squared term: 

Divide each side by '-138405324100000'.
0.0000006584143464 + -21.00000002x + x2 = 0

Move the constant term to the right:

Add '-0.0000006584143464' to each side of the equation.
0.0000006584143464 + -21.00000002x + -0.0000006584143464 + x2 = 0 + -0.0000006584143464

Reorder the terms:
0.0000006584143464 + -0.0000006584143464 + -21.00000002x + x2 = 0 + -0.0000006584143464

Combine like terms: 0.0000006584143464 + -0.0000006584143464 = 0.0000000000000000
0.0000000000000000 + -21.00000002x + x2 = 0 + -0.0000006584143464
-21.00000002x + x2 = 0 + -0.0000006584143464

Combine like terms: 0 + -0.0000006584143464 = -0.0000006584143464
-21.00000002x + x2 = -0.0000006584143464

The x term is -21.00000002x.  Take half its coefficient (-10.50000001).
Square it (110.2500002) and add it to both sides.

Add '110.2500002' to each side of the equation.
-21.00000002x + 110.2500002 + x2 = -0.0000006584143464 + 110.2500002

Reorder the terms:
110.2500002 + -21.00000002x + x2 = -0.0000006584143464 + 110.2500002

Combine like terms: -0.0000006584143464 + 110.2500002 = 110.2499995415856536
110.2500002 + -21.00000002x + x2 = 110.2499995415856536

Factor a perfect square on the left side:
(x + -10.50000001)(x + -10.50000001) = 110.2499995415856536

Calculate the square root of the right side: 10.499999978

Break this problem into two subproblems by setting 
(x + -10.50000001) equal to 10.499999978 and -10.499999978.

Subproblem 1
x + -10.50000001 = 10.499999978

Simplifying
x + -10.50000001 = 10.499999978

Reorder the terms:
-10.50000001 + x = 10.499999978

Solving
-10.50000001 + x = 10.499999978

Solving for variable 'x'.

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

Add '10.50000001' to each side of the equation.
-10.50000001 + 10.50000001 + x = 10.499999978 + 10.50000001

Combine like terms: -10.50000001 + 10.50000001 = 0.00000000
0.00000000 + x = 10.499999978 + 10.50000001
x = 10.499999978 + 10.50000001

Combine like terms: 10.499999978 + 10.50000001 = 20.999999988
x = 20.999999988

Simplifying
x = 20.999999988

Subproblem 2
x + -10.50000001 = -10.499999978

Simplifying
x + -10.50000001 = -10.499999978

Reorder the terms:
-10.50000001 + x = -10.499999978

Solving
-10.50000001 + x = -10.499999978

Solving for variable 'x'.

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

Add '10.50000001' to each side of the equation.
-10.50000001 + 10.50000001 + x = -10.499999978 + 10.50000001

Combine like terms: -10.50000001 + 10.50000001 = 0.00000000
0.00000000 + x = -10.499999978 + 10.50000001
x = -10.499999978 + 10.50000001

Combine like terms: -10.499999978 + 10.50000001 = 0.000000032
x = 0.000000032

Simplifying
x = 0.000000032

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.999999988, 0.000000032}