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

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

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

Reorder the terms:
3 + 2y = 5y(-2y)

Remove parenthesis around (-2y)
3 + 2y = 5y * -2y

Reorder the terms for easier multiplication:
3 + 2y = 5 * -2y * y

Multiply 5 * -2
3 + 2y = -10y * y

Multiply y * y
3 + 2y = -10y2

Solving
3 + 2y = -10y2

Solving for variable 'y'.

Combine like terms: -10y2 + 10y2 = 0
3 + 2y + 10y2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
0.3 + 0.2y + y2 = 0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 0.2y + -0.3 + y2 = 0 + -0.3

Reorder the terms:
0.3 + -0.3 + 0.2y + y2 = 0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 0.2y + y2 = 0 + -0.3
0.2y + y2 = 0 + -0.3

Combine like terms: 0 + -0.3 = -0.3
0.2y + y2 = -0.3

The y term is 0.2y.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2y + 0.01 + y2 = -0.3 + 0.01

Reorder the terms:
0.01 + 0.2y + y2 = -0.3 + 0.01

Combine like terms: -0.3 + 0.01 = -0.29
0.01 + 0.2y + y2 = -0.29

Factor a perfect square on the left side:
(y + 0.1)(y + 0.1) = -0.29

Can't calculate square root of the right side.

The solution to this equation could not be determined.