(3w-10)w=77

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Solution for (3w-10)w=77 equation: 


Simplifying
(3w + -10) * w = 77

Reorder the terms:
(-10 + 3w) * w = 77

Reorder the terms for easier multiplication:
w(-10 + 3w) = 77
(-10 * w + 3w * w) = 77
(-10w + 3w2) = 77

Solving
-10w + 3w2 = 77

Solving for variable 'w'.

Reorder the terms:
-77 + -10w + 3w2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + -10w + 3w2 = 0

Factor a trinomial.
(-11 + -3w)(7 + -1w) = 0


Subproblem 1
Set the factor '(-11 + -3w)' equal to zero and attempt to solve:

Simplifying
-11 + -3w = 0

Solving
-11 + -3w = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3w = 0 + 11
-3w = 0 + 11

Combine like terms: 0 + 11 = 11
-3w = 11

Divide each side by '-3'.
w = -3.666666667

Simplifying
w = -3.666666667

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 = {-3.666666667, 7}

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