4(6w+4)*(5-3)=5(3w+9)*4(6w+8)

Solution for 4(6w+4)*(5-3)=5(3w+9)*4(6w+8) equation:

Simplifying
4(6w + 4)(5 + -3) = 5(3w + 9) * 4(6w + 8)

Reorder the terms:
4(4 + 6w)(5 + -3) = 5(3w + 9) * 4(6w + 8)

Combine like terms: 5 + -3 = 2
4(4 + 6w)(2) = 5(3w + 9) * 4(6w + 8)

Reorder the terms for easier multiplication:
4 * 2(4 + 6w) = 5(3w + 9) * 4(6w + 8)

Multiply 4 * 2
8(4 + 6w) = 5(3w + 9) * 4(6w + 8)
(4 * 8 + 6w * 8) = 5(3w + 9) * 4(6w + 8)
(32 + 48w) = 5(3w + 9) * 4(6w + 8)

Reorder the terms:
32 + 48w = 5(9 + 3w) * 4(6w + 8)

Reorder the terms:
32 + 48w = 5(9 + 3w) * 4(8 + 6w)

Reorder the terms for easier multiplication:
32 + 48w = 5 * 4(9 + 3w)(8 + 6w)

Multiply 5 * 4
32 + 48w = 20(9 + 3w)(8 + 6w)

Multiply (9 + 3w) * (8 + 6w)
32 + 48w = 20(9(8 + 6w) + 3w * (8 + 6w))
32 + 48w = 20((8 * 9 + 6w * 9) + 3w * (8 + 6w))
32 + 48w = 20((72 + 54w) + 3w * (8 + 6w))
32 + 48w = 20(72 + 54w + (8 * 3w + 6w * 3w))
32 + 48w = 20(72 + 54w + (24w + 18w2))

Combine like terms: 54w + 24w = 78w
32 + 48w = 20(72 + 78w + 18w2)
32 + 48w = (72 * 20 + 78w * 20 + 18w2 * 20)
32 + 48w = (1440 + 1560w + 360w2)

Solving
32 + 48w = 1440 + 1560w + 360w2

Solving for variable 'w'.

Reorder the terms:
32 + -1440 + 48w + -1560w + -360w2 = 1440 + 1560w + 360w2 + -1440 + -1560w + -360w2

Combine like terms: 32 + -1440 = -1408
-1408 + 48w + -1560w + -360w2 = 1440 + 1560w + 360w2 + -1440 + -1560w + -360w2

Combine like terms: 48w + -1560w = -1512w
-1408 + -1512w + -360w2 = 1440 + 1560w + 360w2 + -1440 + -1560w + -360w2

Reorder the terms:
-1408 + -1512w + -360w2 = 1440 + -1440 + 1560w + -1560w + 360w2 + -360w2

Combine like terms: 1440 + -1440 = 0
-1408 + -1512w + -360w2 = 0 + 1560w + -1560w + 360w2 + -360w2
-1408 + -1512w + -360w2 = 1560w + -1560w + 360w2 + -360w2

Combine like terms: 1560w + -1560w = 0
-1408 + -1512w + -360w2 = 0 + 360w2 + -360w2
-1408 + -1512w + -360w2 = 360w2 + -360w2

Combine like terms: 360w2 + -360w2 = 0
-1408 + -1512w + -360w2 = 0

Factor out the Greatest Common Factor (GCF), '-8'.
-8(176 + 189w + 45w2) = 0

Ignore the factor -8.
Subproblem 1
Set the factor '(176 + 189w + 45w2)' equal to zero and attempt to solve:

Simplifying
176 + 189w + 45w2 = 0

Solving
176 + 189w + 45w2 = 0

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

Divide each side by '45'.
3.911111111 + 4.2w + w2 = 0

Move the constant term to the right:

Add '-3.911111111' to each side of the equation.
3.911111111 + 4.2w + -3.911111111 + w2 = 0 + -3.911111111

Reorder the terms:
3.911111111 + -3.911111111 + 4.2w + w2 = 0 + -3.911111111

Combine like terms: 3.911111111 + -3.911111111 = 0.000000000
0.000000000 + 4.2w + w2 = 0 + -3.911111111
4.2w + w2 = 0 + -3.911111111

Combine like terms: 0 + -3.911111111 = -3.911111111
4.2w + w2 = -3.911111111

The w term is 4.2w.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2w + 4.41 + w2 = -3.911111111 + 4.41

Reorder the terms:
4.41 + 4.2w + w2 = -3.911111111 + 4.41

Combine like terms: -3.911111111 + 4.41 = 0.498888889
4.41 + 4.2w + w2 = 0.498888889

Factor a perfect square on the left side:
(w + 2.1)(w + 2.1) = 0.498888889

Calculate the square root of the right side: 0.70632067

Break this problem into two subproblems by setting 
(w + 2.1) equal to 0.70632067 and -0.70632067.

Subproblem 1
w + 2.1 = 0.70632067

Simplifying
w + 2.1 = 0.70632067

Reorder the terms:
2.1 + w = 0.70632067

Solving
2.1 + w = 0.70632067

Solving for variable 'w'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + w = 0.70632067 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + w = 0.70632067 + -2.1
w = 0.70632067 + -2.1

Combine like terms: 0.70632067 + -2.1 = -1.39367933
w = -1.39367933

Simplifying
w = -1.39367933

Subproblem 2
w + 2.1 = -0.70632067

Simplifying
w + 2.1 = -0.70632067

Reorder the terms:
2.1 + w = -0.70632067

Solving
2.1 + w = -0.70632067

Solving for variable 'w'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + w = -0.70632067 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + w = -0.70632067 + -2.1
w = -0.70632067 + -2.1

Combine like terms: -0.70632067 + -2.1 = -2.80632067
w = -2.80632067

Simplifying
w = -2.80632067

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.39367933, -2.80632067}
Solution
w = {-1.39367933, -2.80632067}