(24-2w)(32-2w)=609

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Solution for (24-2w)(32-2w)=609 equation: 


Simplifying
(24 + -2w)(32 + -2w) = 609

Multiply (24 + -2w) * (32 + -2w)
(24(32 + -2w) + -2w * (32 + -2w)) = 609
((32 * 24 + -2w * 24) + -2w * (32 + -2w)) = 609
((768 + -48w) + -2w * (32 + -2w)) = 609
(768 + -48w + (32 * -2w + -2w * -2w)) = 609
(768 + -48w + (-64w + 4w2)) = 609

Combine like terms: -48w + -64w = -112w
(768 + -112w + 4w2) = 609

Solving
768 + -112w + 4w2 = 609

Solving for variable 'w'.

Reorder the terms:
768 + -609 + -112w + 4w2 = 609 + -609

Combine like terms: 768 + -609 = 159
159 + -112w + 4w2 = 609 + -609

Combine like terms: 609 + -609 = 0
159 + -112w + 4w2 = 0

Factor a trinomial.
(3 + -2w)(53 + -2w) = 0


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

Simplifying
3 + -2w = 0

Solving
3 + -2w = 0

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

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

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

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

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5

Subproblem 2
Set the factor '(53 + -2w)' equal to zero and attempt to solve:

Simplifying
53 + -2w = 0

Solving
53 + -2w = 0

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

Add '-53' to each side of the equation.
53 + -53 + -2w = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -2w = 0 + -53
-2w = 0 + -53

Combine like terms: 0 + -53 = -53
-2w = -53

Divide each side by '-2'.
w = 26.5

Simplifying
w = 26.5
Solution
w = {1.5, 26.5}

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