=(7x+9y-2x)(8x-3x-3y)

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Solution for =(7x+9y-2x)(8x-3x-3y) equation:


Simplifying
0 = (7x + 9y + -2x)(8x + -3x + -3y)

Reorder the terms:
0 = (7x + -2x + 9y)(8x + -3x + -3y)

Combine like terms: 7x + -2x = 5x
0 = (5x + 9y)(8x + -3x + -3y)

Combine like terms: 8x + -3x = 5x
0 = (5x + 9y)(5x + -3y)

Multiply (5x + 9y) * (5x + -3y)
0 = (5x * (5x + -3y) + 9y * (5x + -3y))
0 = ((5x * 5x + -3y * 5x) + 9y * (5x + -3y))

Reorder the terms:
0 = ((-15xy + 25x2) + 9y * (5x + -3y))
0 = ((-15xy + 25x2) + 9y * (5x + -3y))
0 = (-15xy + 25x2 + (5x * 9y + -3y * 9y))
0 = (-15xy + 25x2 + (45xy + -27y2))

Reorder the terms:
0 = (-15xy + 45xy + 25x2 + -27y2)

Combine like terms: -15xy + 45xy = 30xy
0 = (30xy + 25x2 + -27y2)

Solving
0 = 30xy + 25x2 + -27y2

Solving for variable 'x'.
Remove the zero:
-30xy + -25x2 + 27y2 = 30xy + 25x2 + -27y2 + -30xy + -25x2 + 27y2

Reorder the terms:
-30xy + -25x2 + 27y2 = 30xy + -30xy + 25x2 + -25x2 + -27y2 + 27y2

Combine like terms: 30xy + -30xy = 0
-30xy + -25x2 + 27y2 = 0 + 25x2 + -25x2 + -27y2 + 27y2
-30xy + -25x2 + 27y2 = 25x2 + -25x2 + -27y2 + 27y2

Combine like terms: 25x2 + -25x2 = 0
-30xy + -25x2 + 27y2 = 0 + -27y2 + 27y2
-30xy + -25x2 + 27y2 = -27y2 + 27y2

Combine like terms: -27y2 + 27y2 = 0
-30xy + -25x2 + 27y2 = 0

Factor a trinomial.
(-5x + -9y)(5x + -3y) = 0

Subproblem 1

Set the factor '(-5x + -9y)' equal to zero and attempt to solve: Simplifying -5x + -9y = 0 Solving -5x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. -5x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 -5x + 0 = 0 + 9y -5x = 0 + 9y Remove the zero: -5x = 9y Divide each side by '-5'. x = -1.8y Simplifying x = -1.8y

Subproblem 2

Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6y

Solution

x = {-1.8y, 0.6y}

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