(3w-1)(w-4)=14

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Solution for (3w-1)(w-4)=14 equation: 


Simplifying
(3w + -1)(w + -4) = 14

Reorder the terms:
(-1 + 3w)(w + -4) = 14

Reorder the terms:
(-1 + 3w)(-4 + w) = 14

Multiply (-1 + 3w) * (-4 + w)
(-1(-4 + w) + 3w * (-4 + w)) = 14
((-4 * -1 + w * -1) + 3w * (-4 + w)) = 14
((4 + -1w) + 3w * (-4 + w)) = 14
(4 + -1w + (-4 * 3w + w * 3w)) = 14
(4 + -1w + (-12w + 3w2)) = 14

Combine like terms: -1w + -12w = -13w
(4 + -13w + 3w2) = 14

Solving
4 + -13w + 3w2 = 14

Solving for variable 'w'.

Reorder the terms:
4 + -14 + -13w + 3w2 = 14 + -14

Combine like terms: 4 + -14 = -10
-10 + -13w + 3w2 = 14 + -14

Combine like terms: 14 + -14 = 0
-10 + -13w + 3w2 = 0

Factor a trinomial.
(-2 + -3w)(5 + -1w) = 0


Subproblem 1
Set the factor '(-2 + -3w)' equal to zero and attempt to solve:

Simplifying
-2 + -3w = 0

Solving
-2 + -3w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3w = 0 + 2
-3w = 0 + 2

Combine like terms: 0 + 2 = 2
-3w = 2

Divide each side by '-3'.
w = -0.6666666667

Simplifying
w = -0.6666666667

Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-0.6666666667, 5}

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