7w(2w+3)=5w(3+5)

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Solution for 7w(2w+3)=5w(3+5) equation: 


Simplifying
7w(2w + 3) = 5w(3 + 5)

Reorder the terms:
7w(3 + 2w) = 5w(3 + 5)
(3 * 7w + 2w * 7w) = 5w(3 + 5)
(21w + 14w2) = 5w(3 + 5)

Combine like terms: 3 + 5 = 8
21w + 14w2 = 5w(8)

Reorder the terms for easier multiplication:
21w + 14w2 = 5 * 8w

Multiply 5 * 8
21w + 14w2 = 40w

Solving
21w + 14w2 = 40w

Solving for variable 'w'.

Reorder the terms:
21w + -40w + 14w2 = 40w + -40w

Combine like terms: 21w + -40w = -19w
-19w + 14w2 = 40w + -40w

Combine like terms: 40w + -40w = 0
-19w + 14w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-19 + 14w) = 0


Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

Subproblem 2
Set the factor '(-19 + 14w)' equal to zero and attempt to solve:

Simplifying
-19 + 14w = 0

Solving
-19 + 14w = 0

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

Add '19' to each side of the equation.
-19 + 19 + 14w = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 14w = 0 + 19
14w = 0 + 19

Combine like terms: 0 + 19 = 19
14w = 19

Divide each side by '14'.
w = 1.357142857

Simplifying
w = 1.357142857
Solution
w = {0, 1.357142857}

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