(8x+3y)(4x+7y)=0

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Solution for (8x+3y)(4x+7y)=0 equation: 


Simplifying
(8x + 3y)(4x + 7y) = 0

Multiply (8x + 3y) * (4x + 7y)
(8x * (4x + 7y) + 3y * (4x + 7y)) = 0
((4x * 8x + 7y * 8x) + 3y * (4x + 7y)) = 0

Reorder the terms:
((56xy + 32x2) + 3y * (4x + 7y)) = 0
((56xy + 32x2) + 3y * (4x + 7y)) = 0
(56xy + 32x2 + (4x * 3y + 7y * 3y)) = 0
(56xy + 32x2 + (12xy + 21y2)) = 0

Reorder the terms:
(56xy + 12xy + 32x2 + 21y2) = 0

Combine like terms: 56xy + 12xy = 68xy
(68xy + 32x2 + 21y2) = 0

Solving
68xy + 32x2 + 21y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8x + 3y)(4x + 7y) = 0


Subproblem 1
Set the factor '(8x + 3y)' equal to zero and attempt to solve:

Simplifying
8x + 3y = 0

Solving
8x + 3y = 0

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

Add '-3y' to each side of the equation.
8x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
8x + 0 = 0 + -3y
8x = 0 + -3y
Remove the zero:
8x = -3y

Divide each side by '8'.
x = -0.375y

Simplifying
x = -0.375y

Subproblem 2
Set the factor '(4x + 7y)' equal to zero and attempt to solve:

Simplifying
4x + 7y = 0

Solving
4x + 7y = 0

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

Add '-7y' to each side of the equation.
4x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
4x + 0 = 0 + -7y
4x = 0 + -7y
Remove the zero:
4x = -7y

Divide each side by '4'.
x = -1.75y

Simplifying
x = -1.75y
Solution
x = {-0.375y, -1.75y}

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