5(4r-w)(r-4w)=

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Solution for 5(4r-w)(r-4w)= equation: 


Simplifying
5(4r + -1w)(r + -4w) = 0

Multiply (4r + -1w) * (r + -4w)
5(4r * (r + -4w) + -1w * (r + -4w)) = 0
5((r * 4r + -4w * 4r) + -1w * (r + -4w)) = 0

Reorder the terms:
5((-16rw + 4r2) + -1w * (r + -4w)) = 0
5((-16rw + 4r2) + -1w * (r + -4w)) = 0
5(-16rw + 4r2 + (r * -1w + -4w * -1w)) = 0
5(-16rw + 4r2 + (-1rw + 4w2)) = 0

Reorder the terms:
5(-16rw + -1rw + 4r2 + 4w2) = 0

Combine like terms: -16rw + -1rw = -17rw
5(-17rw + 4r2 + 4w2) = 0
(-17rw * 5 + 4r2 * 5 + 4w2 * 5) = 0
(-85rw + 20r2 + 20w2) = 0

Solving
-85rw + 20r2 + 20w2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-17rw + 4r2 + 4w2) = 0

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

Ignore the factor 5.

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

Simplifying
r + -4w = 0

Solving
r + -4w = 0

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

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

Combine like terms: -4w + 4w = 0
r + 0 = 0 + 4w
r = 0 + 4w
Remove the zero:
r = 4w

Simplifying
r = 4w

Subproblem 2
Set the factor '(4r + -1w)' equal to zero and attempt to solve:

Simplifying
4r + -1w = 0

Solving
4r + -1w = 0

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

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

Combine like terms: -1w + w = 0
4r + 0 = 0 + w
4r = 0 + w
Remove the zero:
4r = w

Divide each side by '4'.
r = 0.25w

Simplifying
r = 0.25w
Solution
r = {4w, 0.25w}

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