6w(5w+2)+w(3w+9)=

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Solution for 6w(5w+2)+w(3w+9)= equation: 


Simplifying
6w(5w + 2) + w(3w + 9) = 0

Reorder the terms:
6w(2 + 5w) + w(3w + 9) = 0
(2 * 6w + 5w * 6w) + w(3w + 9) = 0
(12w + 30w2) + w(3w + 9) = 0

Reorder the terms:
12w + 30w2 + w(9 + 3w) = 0
12w + 30w2 + (9 * w + 3w * w) = 0
12w + 30w2 + (9w + 3w2) = 0

Reorder the terms:
12w + 9w + 30w2 + 3w2 = 0

Combine like terms: 12w + 9w = 21w
21w + 30w2 + 3w2 = 0

Combine like terms: 30w2 + 3w2 = 33w2
21w + 33w2 = 0

Solving
21w + 33w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(7 + 11w) = 0

Ignore the factor 3.

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 '(7 + 11w)' equal to zero and attempt to solve:

Simplifying
7 + 11w = 0

Solving
7 + 11w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 11w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 11w = 0 + -7
11w = 0 + -7

Combine like terms: 0 + -7 = -7
11w = -7

Divide each side by '11'.
w = -0.6363636364

Simplifying
w = -0.6363636364
Solution
w = {0, -0.6363636364}

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