-(5x+2y)(5x+3y)=

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

Simplifying
-1(5x + 2y)(5x + 3y) = 0

Multiply (5x + 2y) * (5x + 3y)
-1(5x * (5x + 3y) + 2y * (5x + 3y)) = 0
-1((5x * 5x + 3y * 5x) + 2y * (5x + 3y)) = 0

Reorder the terms:
-1((15xy + 25x2) + 2y * (5x + 3y)) = 0
-1((15xy + 25x2) + 2y * (5x + 3y)) = 0
-1(15xy + 25x2 + (5x * 2y + 3y * 2y)) = 0
-1(15xy + 25x2 + (10xy + 6y2)) = 0

Reorder the terms:
-1(15xy + 10xy + 25x2 + 6y2) = 0

Combine like terms: 15xy + 10xy = 25xy
-1(25xy + 25x2 + 6y2) = 0
(25xy * -1 + 25x2 * -1 + 6y2 * -1) = 0
(-25xy + -25x2 + -6y2) = 0

Solving
-25xy + -25x2 + -6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25xy + 25x2 + 6y2) = 0

Factor a trinomial.
-1((5x + 2y)(5x + 3y)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

Add '-2y' to each side of the equation.
5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
5x + 0 = 0 + -2y
5x = 0 + -2y
Remove the zero:
5x = -2y

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y
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 = {-0.4y, -0.6y}