Answer:
Simplifying
5x(2x + y) = 0
(2x * 5x + y * 5x) = 0
Reorder the terms:
(5xy + 10x2) = 0
(5xy + 10x2) = 0
Solving
5xy + 10x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '5x'.
5x(y + 2x) = 0
Ignore the factor 5.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(y + 2x)' equal to zero and attempt to solve:
Simplifying
y + 2x = 0
Reorder the terms:
2x + y = 0
Solving
2x + y = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y
Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y
Divide each side by '2'.
x = -0.5y
Simplifying
x = -0.5y
Solution
x = {0, -0.5y}