30(15-x)3x+50x=490

Solution for 30(15-x)3x+50x=490 equation:

Simplifying
30(15 + -1x) * 3x + 50x = 490

Reorder the terms for easier multiplication:
30 * 3x(15 + -1x) + 50x = 490

Multiply 30 * 3
90x(15 + -1x) + 50x = 490
(15 * 90x + -1x * 90x) + 50x = 490
(1350x + -90x2) + 50x = 490

Reorder the terms:
1350x + 50x + -90x2 = 490

Combine like terms: 1350x + 50x = 1400x
1400x + -90x2 = 490

Solving
1400x + -90x2 = 490

Solving for variable 'x'.

Reorder the terms:
-490 + 1400x + -90x2 = 490 + -490

Combine like terms: 490 + -490 = 0
-490 + 1400x + -90x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-49 + 140x + -9x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-49 + 140x + -9x2)' equal to zero and attempt to solve:

Simplifying
-49 + 140x + -9x2 = 0

Solving
-49 + 140x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
5.444444444 + -15.55555556x + x2 = 0

Move the constant term to the right:

Add '-5.444444444' to each side of the equation.
5.444444444 + -15.55555556x + -5.444444444 + x2 = 0 + -5.444444444

Reorder the terms:
5.444444444 + -5.444444444 + -15.55555556x + x2 = 0 + -5.444444444

Combine like terms: 5.444444444 + -5.444444444 = 0.000000000
0.000000000 + -15.55555556x + x2 = 0 + -5.444444444
-15.55555556x + x2 = 0 + -5.444444444

Combine like terms: 0 + -5.444444444 = -5.444444444
-15.55555556x + x2 = -5.444444444

The x term is -15.55555556x.  Take half its coefficient (-7.77777778).
Square it (60.49382720) and add it to both sides.

Add '60.49382720' to each side of the equation.
-15.55555556x + 60.49382720 + x2 = -5.444444444 + 60.49382720

Reorder the terms:
60.49382720 + -15.55555556x + x2 = -5.444444444 + 60.49382720

Combine like terms: -5.444444444 + 60.49382720 = 55.049382756
60.49382720 + -15.55555556x + x2 = 55.049382756

Factor a perfect square on the left side:
(x + -7.77777778)(x + -7.77777778) = 55.049382756

Calculate the square root of the right side: 7.419527125

Break this problem into two subproblems by setting 
(x + -7.77777778) equal to 7.419527125 and -7.419527125.

Subproblem 1
x + -7.77777778 = 7.419527125

Simplifying
x + -7.77777778 = 7.419527125

Reorder the terms:
-7.77777778 + x = 7.419527125

Solving
-7.77777778 + x = 7.419527125

Solving for variable 'x'.

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

Add '7.77777778' to each side of the equation.
-7.77777778 + 7.77777778 + x = 7.419527125 + 7.77777778

Combine like terms: -7.77777778 + 7.77777778 = 0.00000000
0.00000000 + x = 7.419527125 + 7.77777778
x = 7.419527125 + 7.77777778

Combine like terms: 7.419527125 + 7.77777778 = 15.197304905
x = 15.197304905

Simplifying
x = 15.197304905

Subproblem 2
x + -7.77777778 = -7.419527125

Simplifying
x + -7.77777778 = -7.419527125

Reorder the terms:
-7.77777778 + x = -7.419527125

Solving
-7.77777778 + x = -7.419527125

Solving for variable 'x'.

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

Add '7.77777778' to each side of the equation.
-7.77777778 + 7.77777778 + x = -7.419527125 + 7.77777778

Combine like terms: -7.77777778 + 7.77777778 = 0.00000000
0.00000000 + x = -7.419527125 + 7.77777778
x = -7.419527125 + 7.77777778

Combine like terms: -7.419527125 + 7.77777778 = 0.358250655
x = 0.358250655

Simplifying
x = 0.358250655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.197304905, 0.358250655}
Solution
x = {15.197304905, 0.358250655}