(4x+5w)(4x-w)=0

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Solution for (4x+5w)(4x-w)=0 equation: 


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

Reorder the terms:
(5w + 4x)(4x + -1w) = 0

Reorder the terms:
(5w + 4x)(-1w + 4x) = 0

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

Reorder the terms:
((20wx + -5w2) + 4x * (-1w + 4x)) = 0
((20wx + -5w2) + 4x * (-1w + 4x)) = 0
(20wx + -5w2 + (-1w * 4x + 4x * 4x)) = 0
(20wx + -5w2 + (-4wx + 16x2)) = 0

Reorder the terms:
(20wx + -4wx + -5w2 + 16x2) = 0

Combine like terms: 20wx + -4wx = 16wx
(16wx + -5w2 + 16x2) = 0

Solving
16wx + -5w2 + 16x2 = 0

Solving for variable 'w'.

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


Subproblem 1
Set the factor '(-5w + -4x)' equal to zero and attempt to solve:

Simplifying
-5w + -4x = 0

Solving
-5w + -4x = 0

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

Add '4x' to each side of the equation.
-5w + -4x + 4x = 0 + 4x

Combine like terms: -4x + 4x = 0
-5w + 0 = 0 + 4x
-5w = 0 + 4x
Remove the zero:
-5w = 4x

Divide each side by '-5'.
w = -0.8x

Simplifying
w = -0.8x

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

Simplifying
w + -4x = 0

Solving
w + -4x = 0

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

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

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

Simplifying
w = 4x
Solution
w = {-0.8x, 4x}

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