1-(5-2y)(2y+3)=

Solution for 1-(5-2y)(2y+3)= equation:

Simplifying
1 + -1(5 + -2y)(2y + 3) = 0

Reorder the terms:
1 + -1(5 + -2y)(3 + 2y) = 0

Multiply (5 + -2y) * (3 + 2y)
1 + -1(5(3 + 2y) + -2y * (3 + 2y)) = 0
1 + -1((3 * 5 + 2y * 5) + -2y * (3 + 2y)) = 0
1 + -1((15 + 10y) + -2y * (3 + 2y)) = 0
1 + -1(15 + 10y + (3 * -2y + 2y * -2y)) = 0
1 + -1(15 + 10y + (-6y + -4y2)) = 0

Combine like terms: 10y + -6y = 4y
1 + -1(15 + 4y + -4y2) = 0
1 + (15 * -1 + 4y * -1 + -4y2 * -1) = 0
1 + (-15 + -4y + 4y2) = 0

Combine like terms: 1 + -15 = -14
-14 + -4y + 4y2 = 0

Solving
-14 + -4y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -2y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -2y + 2y2)' equal to zero and attempt to solve:

Simplifying
-7 + -2y + 2y2 = 0

Solving
-7 + -2y + 2y2 = 0

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

Divide each side by '2'.
-3.5 + -1y + y2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -1y + 3.5 + y2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -1y + y2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -1y + y2 = 0 + 3.5
-1y + y2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-1y + y2 = 3.5

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 3.5 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
0.25 + -1y + y2 = 3.75

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(y + -0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
y + -0.5 = 1.936491673

Simplifying
y + -0.5 = 1.936491673

Reorder the terms:
-0.5 + y = 1.936491673

Solving
-0.5 + y = 1.936491673

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 1.936491673 + 0.5
y = 1.936491673 + 0.5

Combine like terms: 1.936491673 + 0.5 = 2.436491673
y = 2.436491673

Simplifying
y = 2.436491673

Subproblem 2
y + -0.5 = -1.936491673

Simplifying
y + -0.5 = -1.936491673

Reorder the terms:
-0.5 + y = -1.936491673

Solving
-0.5 + y = -1.936491673

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -1.936491673 + 0.5
y = -1.936491673 + 0.5

Combine like terms: -1.936491673 + 0.5 = -1.436491673
y = -1.436491673

Simplifying
y = -1.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.436491673, -1.436491673}
Solution
y = {2.436491673, -1.436491673}