(10x^2)(y^2)-55xy^2-150y^2=0

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Solution for (10x^2)(y^2)-55xy^2-150y^2=0 equation: 


Simplifying
(10x2)(y2) + -55xy2 + -150y2 = 0

Remove parenthesis around (10x2)
10x2(y2) + -55xy2 + -150y2 = 0

Multiply x2 * y2
10x2y2 + -55xy2 + -150y2 = 0

Reorder the terms:
-55xy2 + 10x2y2 + -150y2 = 0

Solving
-55xy2 + 10x2y2 + -150y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(-11x + 2x2 + -30) = 0

Factor a trinomial.
5y2((2x + -15)(x + 2)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = 0 + -1y2
Remove the zero:
0 = -1y2

Simplifying
0 = -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2x + -15)' equal to zero and attempt to solve:

Simplifying
2x + -15 = 0

Reorder the terms:
-15 + 2x = 0

Solving
-15 + 2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 0 + 15
2x = 0 + 15

Combine like terms: 0 + 15 = 15
2x = 15

Divide each side by '2'.
x = 7.5

Simplifying
x = 7.5

Subproblem 3
Set the factor '(x + 2)' equal to zero and attempt to solve:

Simplifying
x + 2 = 0

Reorder the terms:
2 + x = 0

Solving
2 + x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {7.5, -2}

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