(4x+5y)(3x+8y)=

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Solution for (4x+5y)(3x+8y)= equation: 


Simplifying
(4x + 5y)(3x + 8y) = 0

Multiply (4x + 5y) * (3x + 8y)
(4x * (3x + 8y) + 5y * (3x + 8y)) = 0
((3x * 4x + 8y * 4x) + 5y * (3x + 8y)) = 0

Reorder the terms:
((32xy + 12x2) + 5y * (3x + 8y)) = 0
((32xy + 12x2) + 5y * (3x + 8y)) = 0
(32xy + 12x2 + (3x * 5y + 8y * 5y)) = 0
(32xy + 12x2 + (15xy + 40y2)) = 0

Reorder the terms:
(32xy + 15xy + 12x2 + 40y2) = 0

Combine like terms: 32xy + 15xy = 47xy
(47xy + 12x2 + 40y2) = 0

Solving
47xy + 12x2 + 40y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + 5y)(3x + 8y) = 0


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

Simplifying
4x + 5y = 0

Solving
4x + 5y = 0

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

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

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

Divide each side by '4'.
x = -1.25y

Simplifying
x = -1.25y

Subproblem 2
Set the factor '(3x + 8y)' equal to zero and attempt to solve:

Simplifying
3x + 8y = 0

Solving
3x + 8y = 0

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

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

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

Divide each side by '3'.
x = -2.666666667y

Simplifying
x = -2.666666667y
Solution
x = {-1.25y, -2.666666667y}

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