2(1-2y)=5y(y+1)

Solution for 2(1-2y)=5y(y+1) equation:

Simplifying
2(1 + -2y) = 5y(y + 1)
(1 * 2 + -2y * 2) = 5y(y + 1)
(2 + -4y) = 5y(y + 1)

Reorder the terms:
2 + -4y = 5y(1 + y)
2 + -4y = (1 * 5y + y * 5y)
2 + -4y = (5y + 5y2)

Solving
2 + -4y = 5y + 5y2

Solving for variable 'y'.

Combine like terms: -4y + -5y = -9y
2 + -9y + -5y2 = 5y + 5y2 + -5y + -5y2

Reorder the terms:
2 + -9y + -5y2 = 5y + -5y + 5y2 + -5y2

Combine like terms: 5y + -5y = 0
2 + -9y + -5y2 = 0 + 5y2 + -5y2
2 + -9y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
2 + -9y + -5y2 = 0

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

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

Simplifying
1 + -5y = 0

Solving
1 + -5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {0.2, -2}