(2w-3)(w)=14

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Solution for (2w-3)(w)=14 equation: 


Simplifying
(2w + -3)(w) = 14

Reorder the terms:
(-3 + 2w)(w) = 14

Reorder the terms for easier multiplication:
w(-3 + 2w) = 14
(-3 * w + 2w * w) = 14
(-3w + 2w2) = 14

Solving
-3w + 2w2 = 14

Solving for variable 'w'.

Reorder the terms:
-14 + -3w + 2w2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -3w + 2w2 = 0

Factor a trinomial.
(-2 + -1w)(7 + -2w) = 0


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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 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 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2

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

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Solution
w = {-2, 3.5}

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