(3x+2y)*(4x+5y)=

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Solution for (3x+2y)*(4x+5y)= equation: 


Simplifying
(3x + 2y)(4x + 5y) = 0

Multiply (3x + 2y) * (4x + 5y)
(3x * (4x + 5y) + 2y * (4x + 5y)) = 0
((4x * 3x + 5y * 3x) + 2y * (4x + 5y)) = 0

Reorder the terms:
((15xy + 12x2) + 2y * (4x + 5y)) = 0
((15xy + 12x2) + 2y * (4x + 5y)) = 0
(15xy + 12x2 + (4x * 2y + 5y * 2y)) = 0
(15xy + 12x2 + (8xy + 10y2)) = 0

Reorder the terms:
(15xy + 8xy + 12x2 + 10y2) = 0

Combine like terms: 15xy + 8xy = 23xy
(23xy + 12x2 + 10y2) = 0

Solving
23xy + 12x2 + 10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + 2y)(4x + 5y) = 0


Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve:

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

Subproblem 2
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
Solution
x = {-0.6666666667y, -1.25y}

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