y^2+(1-2y)(1+2y)=y(y-3)

Solution for y^2+(1-2y)(1+2y)=y(y-3) equation:

Simplifying
y2 + (1 + -2y)(1 + 2y) = y(y + -3)

Multiply (1 + -2y) * (1 + 2y)
y2 + (1(1 + 2y) + -2y * (1 + 2y)) = y(y + -3)
y2 + ((1 * 1 + 2y * 1) + -2y * (1 + 2y)) = y(y + -3)
y2 + ((1 + 2y) + -2y * (1 + 2y)) = y(y + -3)
y2 + (1 + 2y + (1 * -2y + 2y * -2y)) = y(y + -3)
y2 + (1 + 2y + (-2y + -4y2)) = y(y + -3)

Combine like terms: 2y + -2y = 0
y2 + (1 + 0 + -4y2) = y(y + -3)
y2 + (1 + -4y2) = y(y + -3)

Reorder the terms:
1 + y2 + -4y2 = y(y + -3)

Combine like terms: y2 + -4y2 = -3y2
1 + -3y2 = y(y + -3)

Reorder the terms:
1 + -3y2 = y(-3 + y)
1 + -3y2 = (-3 * y + y * y)
1 + -3y2 = (-3y + y2)

Solving
1 + -3y2 = -3y + y2

Solving for variable 'y'.

Reorder the terms:
1 + 3y + -3y2 + -1y2 = -3y + y2 + 3y + -1y2

Combine like terms: -3y2 + -1y2 = -4y2
1 + 3y + -4y2 = -3y + y2 + 3y + -1y2

Reorder the terms:
1 + 3y + -4y2 = -3y + 3y + y2 + -1y2

Combine like terms: -3y + 3y = 0
1 + 3y + -4y2 = 0 + y2 + -1y2
1 + 3y + -4y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
1 + 3y + -4y2 = 0

Factor a trinomial.
(1 + -1y)(1 + 4y) = 0

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 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 + 4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y = 0 + -1
4y = 0 + -1

Combine like terms: 0 + -1 = -1
4y = -1

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {1, -0.25}