(3w+9)(w)=210

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Solution for (3w+9)(w)=210 equation: 


Simplifying
(3w + 9)(w) = 210

Reorder the terms:
(9 + 3w)(w) = 210

Reorder the terms for easier multiplication:
w(9 + 3w) = 210
(9 * w + 3w * w) = 210
(9w + 3w2) = 210

Solving
9w + 3w2 = 210

Solving for variable 'w'.

Reorder the terms:
-210 + 9w + 3w2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 9w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-70 + 3w + w2) = 0

Factor a trinomial.
3((-10 + -1w)(7 + -1w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10

Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {-10, 7}

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