(4X-5Y)(2X+7Y)=

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Solution for (4X-5Y)(2X+7Y)= equation: 


Simplifying
(4X + -5Y)(2X + 7Y) = 0

Multiply (4X + -5Y) * (2X + 7Y)
(4X * (2X + 7Y) + -5Y * (2X + 7Y)) = 0
((2X * 4X + 7Y * 4X) + -5Y * (2X + 7Y)) = 0

Reorder the terms:
((28XY + 8X2) + -5Y * (2X + 7Y)) = 0
((28XY + 8X2) + -5Y * (2X + 7Y)) = 0
(28XY + 8X2 + (2X * -5Y + 7Y * -5Y)) = 0
(28XY + 8X2 + (-10XY + -35Y2)) = 0

Reorder the terms:
(28XY + -10XY + 8X2 + -35Y2) = 0

Combine like terms: 28XY + -10XY = 18XY
(18XY + 8X2 + -35Y2) = 0

Solving
18XY + 8X2 + -35Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(4X + -5Y)(2X + 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 '(2X + 7Y)' equal to zero and attempt to solve:

Simplifying
2X + 7Y = 0

Solving
2X + 7Y = 0

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

Add '-7Y' to each side of the equation.
2X + 7Y + -7Y = 0 + -7Y

Combine like terms: 7Y + -7Y = 0
2X + 0 = 0 + -7Y
2X = 0 + -7Y
Remove the zero:
2X = -7Y

Divide each side by '2'.
X = -3.5Y

Simplifying
X = -3.5Y
Solution
X = {1.25Y, -3.5Y}

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