(40-2w)(28-2w)=640

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Solution for (40-2w)(28-2w)=640 equation:


Simplifying
(40 + -2w)(28 + -2w) = 640

Multiply (40 + -2w) * (28 + -2w)
(40(28 + -2w) + -2w * (28 + -2w)) = 640
((28 * 40 + -2w * 40) + -2w * (28 + -2w)) = 640
((1120 + -80w) + -2w * (28 + -2w)) = 640
(1120 + -80w + (28 * -2w + -2w * -2w)) = 640
(1120 + -80w + (-56w + 4w2)) = 640

Combine like terms: -80w + -56w = -136w
(1120 + -136w + 4w2) = 640

Solving
1120 + -136w + 4w2 = 640

Solving for variable 'w'.

Reorder the terms:
1120 + -640 + -136w + 4w2 = 640 + -640

Combine like terms: 1120 + -640 = 480
480 + -136w + 4w2 = 640 + -640

Combine like terms: 640 + -640 = 0
480 + -136w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(120 + -34w + w2) = 0

Factor a trinomial.
4((4 + -1w)(30 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4

Subproblem 2
Set the factor '(30 + -1w)' equal to zero and attempt to solve:

Simplifying
30 + -1w = 0

Solving
30 + -1w = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1w = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1w = 0 + -30
-1w = 0 + -30

Combine like terms: 0 + -30 = -30
-1w = -30

Divide each side by '-1'.
w = 30

Simplifying
w = 30
Solution
w = {4, 30}

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