(W^2+10w+21)(6w-18)=0

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Solution for (W^2+10w+21)(6w-18)=0 equation: 


Simplifying
(W2 + 10w + 21)(6w + -18) = 0

Reorder the terms:
(21 + W2 + 10w)(6w + -18) = 0

Reorder the terms:
(21 + W2 + 10w)(-18 + 6w) = 0

Multiply (21 + W2 + 10w) * (-18 + 6w)
(21(-18 + 6w) + W2(-18 + 6w) + 10w * (-18 + 6w)) = 0
((-18 * 21 + 6w * 21) + W2(-18 + 6w) + 10w * (-18 + 6w)) = 0
((-378 + 126w) + W2(-18 + 6w) + 10w * (-18 + 6w)) = 0
(-378 + 126w + (-18 * W2 + 6w * W2) + 10w * (-18 + 6w)) = 0
(-378 + 126w + (-18W2 + 6wW2) + 10w * (-18 + 6w)) = 0
(-378 + 126w + -18W2 + 6wW2 + (-18 * 10w + 6w * 10w)) = 0
(-378 + 126w + -18W2 + 6wW2 + (-180w + 60w2)) = 0

Reorder the terms:
(-378 + -18W2 + 126w + -180w + 6wW2 + 60w2) = 0

Combine like terms: 126w + -180w = -54w
(-378 + -18W2 + -54w + 6wW2 + 60w2) = 0

Solving
-378 + -18W2 + -54w + 6wW2 + 60w2 = 0

Solving for variable 'W'.

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

Add '378' to each side of the equation.
-378 + -18W2 + -54w + 6wW2 + 378 + 60w2 = 0 + 378

Reorder the terms:
-378 + 378 + -18W2 + -54w + 6wW2 + 60w2 = 0 + 378

Combine like terms: -378 + 378 = 0
0 + -18W2 + -54w + 6wW2 + 60w2 = 0 + 378
-18W2 + -54w + 6wW2 + 60w2 = 0 + 378

Combine like terms: 0 + 378 = 378
-18W2 + -54w + 6wW2 + 60w2 = 378

Add '54w' to each side of the equation.
-18W2 + -54w + 6wW2 + 54w + 60w2 = 378 + 54w

Reorder the terms:
-18W2 + -54w + 54w + 6wW2 + 60w2 = 378 + 54w

Combine like terms: -54w + 54w = 0
-18W2 + 0 + 6wW2 + 60w2 = 378 + 54w
-18W2 + 6wW2 + 60w2 = 378 + 54w

Add '-60w2' to each side of the equation.
-18W2 + 6wW2 + 60w2 + -60w2 = 378 + 54w + -60w2

Combine like terms: 60w2 + -60w2 = 0
-18W2 + 6wW2 + 0 = 378 + 54w + -60w2
-18W2 + 6wW2 = 378 + 54w + -60w2

Reorder the terms:
-378 + -18W2 + -54w + 6wW2 + 60w2 = 378 + 54w + -60w2 + -378 + -54w + 60w2

Reorder the terms:
-378 + -18W2 + -54w + 6wW2 + 60w2 = 378 + -378 + 54w + -54w + -60w2 + 60w2

Combine like terms: 378 + -378 = 0
-378 + -18W2 + -54w + 6wW2 + 60w2 = 0 + 54w + -54w + -60w2 + 60w2
-378 + -18W2 + -54w + 6wW2 + 60w2 = 54w + -54w + -60w2 + 60w2

Combine like terms: 54w + -54w = 0
-378 + -18W2 + -54w + 6wW2 + 60w2 = 0 + -60w2 + 60w2
-378 + -18W2 + -54w + 6wW2 + 60w2 = -60w2 + 60w2

Combine like terms: -60w2 + 60w2 = 0
-378 + -18W2 + -54w + 6wW2 + 60w2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-63 + -3W2 + -9w + wW2 + 10w2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-63 + -3W2 + -9w + wW2 + 10w2)' equal to zero and attempt to solve:

Simplifying
-63 + -3W2 + -9w + wW2 + 10w2 = 0

Solving
-63 + -3W2 + -9w + wW2 + 10w2 = 0

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

Add '63' to each side of the equation.
-63 + -3W2 + -9w + wW2 + 63 + 10w2 = 0 + 63

Reorder the terms:
-63 + 63 + -3W2 + -9w + wW2 + 10w2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -3W2 + -9w + wW2 + 10w2 = 0 + 63
-3W2 + -9w + wW2 + 10w2 = 0 + 63

Combine like terms: 0 + 63 = 63
-3W2 + -9w + wW2 + 10w2 = 63

Add '9w' to each side of the equation.
-3W2 + -9w + wW2 + 9w + 10w2 = 63 + 9w

Reorder the terms:
-3W2 + -9w + 9w + wW2 + 10w2 = 63 + 9w

Combine like terms: -9w + 9w = 0
-3W2 + 0 + wW2 + 10w2 = 63 + 9w
-3W2 + wW2 + 10w2 = 63 + 9w

Add '-10w2' to each side of the equation.
-3W2 + wW2 + 10w2 + -10w2 = 63 + 9w + -10w2

Combine like terms: 10w2 + -10w2 = 0
-3W2 + wW2 + 0 = 63 + 9w + -10w2
-3W2 + wW2 = 63 + 9w + -10w2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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