(5x+3y)(3x-y)=

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


Simplifying
(5x + 3y)(3x + -1y) = 0

Multiply (5x + 3y) * (3x + -1y)
(5x * (3x + -1y) + 3y * (3x + -1y)) = 0
((3x * 5x + -1y * 5x) + 3y * (3x + -1y)) = 0

Reorder the terms:
((-5xy + 15x2) + 3y * (3x + -1y)) = 0
((-5xy + 15x2) + 3y * (3x + -1y)) = 0
(-5xy + 15x2 + (3x * 3y + -1y * 3y)) = 0
(-5xy + 15x2 + (9xy + -3y2)) = 0

Reorder the terms:
(-5xy + 9xy + 15x2 + -3y2) = 0

Combine like terms: -5xy + 9xy = 4xy
(4xy + 15x2 + -3y2) = 0

Solving
4xy + 15x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -1y)(5x + 3y) = 0

Subproblem 1

Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333y

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 = {0.3333333333y, -0.6y}

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