(8w+4x)(5w-6x)=0

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Solution for (8w+4x)(5w-6x)=0 equation: 


Simplifying
(8w + 4x)(5w + -6x) = 0

Multiply (8w + 4x) * (5w + -6x)
(8w * (5w + -6x) + 4x * (5w + -6x)) = 0
((5w * 8w + -6x * 8w) + 4x * (5w + -6x)) = 0

Reorder the terms:
((-48wx + 40w2) + 4x * (5w + -6x)) = 0
((-48wx + 40w2) + 4x * (5w + -6x)) = 0
(-48wx + 40w2 + (5w * 4x + -6x * 4x)) = 0
(-48wx + 40w2 + (20wx + -24x2)) = 0

Reorder the terms:
(-48wx + 20wx + 40w2 + -24x2) = 0

Combine like terms: -48wx + 20wx = -28wx
(-28wx + 40w2 + -24x2) = 0

Solving
-28wx + 40w2 + -24x2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7wx + 10w2 + -6x2) = 0

Factor a trinomial.
4((5w + -6x)(2w + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5w + -6x)' equal to zero and attempt to solve:

Simplifying
5w + -6x = 0

Solving
5w + -6x = 0

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

Add '6x' to each side of the equation.
5w + -6x + 6x = 0 + 6x

Combine like terms: -6x + 6x = 0
5w + 0 = 0 + 6x
5w = 0 + 6x
Remove the zero:
5w = 6x

Divide each side by '5'.
w = 1.2x

Simplifying
w = 1.2x

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

Simplifying
2w + x = 0

Solving
2w + x = 0

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

Add '-1x' to each side of the equation.
2w + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2w + 0 = 0 + -1x
2w = 0 + -1x
Remove the zero:
2w = -1x

Divide each side by '2'.
w = -0.5x

Simplifying
w = -0.5x
Solution
w = {1.2x, -0.5x}

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