(4x-5y)(6x+7y)=

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Solution for (4x-5y)(6x+7y)= equation: 


Simplifying
(4x + -5y)(6x + 7y) = 0

Multiply (4x + -5y) * (6x + 7y)
(4x * (6x + 7y) + -5y * (6x + 7y)) = 0
((6x * 4x + 7y * 4x) + -5y * (6x + 7y)) = 0

Reorder the terms:
((28xy + 24x2) + -5y * (6x + 7y)) = 0
((28xy + 24x2) + -5y * (6x + 7y)) = 0
(28xy + 24x2 + (6x * -5y + 7y * -5y)) = 0
(28xy + 24x2 + (-30xy + -35y2)) = 0

Reorder the terms:
(28xy + -30xy + 24x2 + -35y2) = 0

Combine like terms: 28xy + -30xy = -2xy
(-2xy + 24x2 + -35y2) = 0

Solving
-2xy + 24x2 + -35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -5y)(6x + 7y) = 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 '(6x + 7y)' equal to zero and attempt to solve:

Simplifying
6x + 7y = 0

Solving
6x + 7y = 0

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

Add '-7y' to each side of the equation.
6x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
6x + 0 = 0 + -7y
6x = 0 + -7y
Remove the zero:
6x = -7y

Divide each side by '6'.
x = -1.166666667y

Simplifying
x = -1.166666667y
Solution
x = {1.25y, -1.166666667y}

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