5(2w+3)10w=6(4w+1)

Solution for 5(2w+3)10w=6(4w+1) equation:

Simplifying
5(2w + 3) * 10w = 6(4w + 1)

Reorder the terms:
5(3 + 2w) * 10w = 6(4w + 1)

Reorder the terms for easier multiplication:
5 * 10w(3 + 2w) = 6(4w + 1)

Multiply 5 * 10
50w(3 + 2w) = 6(4w + 1)
(3 * 50w + 2w * 50w) = 6(4w + 1)
(150w + 100w2) = 6(4w + 1)

Reorder the terms:
150w + 100w2 = 6(1 + 4w)
150w + 100w2 = (1 * 6 + 4w * 6)
150w + 100w2 = (6 + 24w)

Solving
150w + 100w2 = 6 + 24w

Solving for variable 'w'.

Reorder the terms:
-6 + 150w + -24w + 100w2 = 6 + 24w + -6 + -24w

Combine like terms: 150w + -24w = 126w
-6 + 126w + 100w2 = 6 + 24w + -6 + -24w

Reorder the terms:
-6 + 126w + 100w2 = 6 + -6 + 24w + -24w

Combine like terms: 6 + -6 = 0
-6 + 126w + 100w2 = 0 + 24w + -24w
-6 + 126w + 100w2 = 24w + -24w

Combine like terms: 24w + -24w = 0
-6 + 126w + 100w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 63w + 50w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 63w + 50w2)' equal to zero and attempt to solve:

Simplifying
-3 + 63w + 50w2 = 0

Solving
-3 + 63w + 50w2 = 0

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

Divide each side by '50'.
-0.06 + 1.26w + w2 = 0.0

Move the constant term to the right:

Add '0.06' to each side of the equation.
-0.06 + 1.26w + 0.06 + w2 = 0.0 + 0.06

Reorder the terms:
-0.06 + 0.06 + 1.26w + w2 = 0.0 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + 1.26w + w2 = 0.0 + 0.06
1.26w + w2 = 0.0 + 0.06

Combine like terms: 0.0 + 0.06 = 0.06
1.26w + w2 = 0.06

The w term is 1.26w.  Take half its coefficient (0.63).
Square it (0.3969) and add it to both sides.

Add '0.3969' to each side of the equation.
1.26w + 0.3969 + w2 = 0.06 + 0.3969

Reorder the terms:
0.3969 + 1.26w + w2 = 0.06 + 0.3969

Combine like terms: 0.06 + 0.3969 = 0.4569
0.3969 + 1.26w + w2 = 0.4569

Factor a perfect square on the left side:
(w + 0.63)(w + 0.63) = 0.4569

Calculate the square root of the right side: 0.675943785

Break this problem into two subproblems by setting 
(w + 0.63) equal to 0.675943785 and -0.675943785.

Subproblem 1
w + 0.63 = 0.675943785

Simplifying
w + 0.63 = 0.675943785

Reorder the terms:
0.63 + w = 0.675943785

Solving
0.63 + w = 0.675943785

Solving for variable 'w'.

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

Add '-0.63' to each side of the equation.
0.63 + -0.63 + w = 0.675943785 + -0.63

Combine like terms: 0.63 + -0.63 = 0.00
0.00 + w = 0.675943785 + -0.63
w = 0.675943785 + -0.63

Combine like terms: 0.675943785 + -0.63 = 0.045943785
w = 0.045943785

Simplifying
w = 0.045943785

Subproblem 2
w + 0.63 = -0.675943785

Simplifying
w + 0.63 = -0.675943785

Reorder the terms:
0.63 + w = -0.675943785

Solving
0.63 + w = -0.675943785

Solving for variable 'w'.

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

Add '-0.63' to each side of the equation.
0.63 + -0.63 + w = -0.675943785 + -0.63

Combine like terms: 0.63 + -0.63 = 0.00
0.00 + w = -0.675943785 + -0.63
w = -0.675943785 + -0.63

Combine like terms: -0.675943785 + -0.63 = -1.305943785
w = -1.305943785

Simplifying
w = -1.305943785

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.045943785, -1.305943785}
Solution
w = {0.045943785, -1.305943785}