(y+4)(y+1)=y-(y-2)(2-y)

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Solution for (y+4)(y+1)=y-(y-2)(2-y) equation: 


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

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

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

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

Combine like terms: 4y + 1y = 5y
(4 + 5y + y2) = y + -1(y + -2)(2 + -1y)

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

Multiply (-2 + y) * (2 + -1y)
4 + 5y + y2 = y + -1(-2(2 + -1y) + y(2 + -1y))
4 + 5y + y2 = y + -1((2 * -2 + -1y * -2) + y(2 + -1y))
4 + 5y + y2 = y + -1((-4 + 2y) + y(2 + -1y))
4 + 5y + y2 = y + -1(-4 + 2y + (2 * y + -1y * y))
4 + 5y + y2 = y + -1(-4 + 2y + (2y + -1y2))

Combine like terms: 2y + 2y = 4y
4 + 5y + y2 = y + -1(-4 + 4y + -1y2)
4 + 5y + y2 = y + (-4 * -1 + 4y * -1 + -1y2 * -1)
4 + 5y + y2 = y + (4 + -4y + 1y2)

Reorder the terms:
4 + 5y + y2 = 4 + y + -4y + 1y2

Combine like terms: y + -4y = -3y
4 + 5y + y2 = 4 + -3y + 1y2

Add '-4' to each side of the equation.
4 + 5y + -4 + y2 = 4 + -3y + -4 + 1y2

Reorder the terms:
4 + -4 + 5y + y2 = 4 + -3y + -4 + 1y2

Combine like terms: 4 + -4 = 0
0 + 5y + y2 = 4 + -3y + -4 + 1y2
5y + y2 = 4 + -3y + -4 + 1y2

Reorder the terms:
5y + y2 = 4 + -4 + -3y + 1y2

Combine like terms: 4 + -4 = 0
5y + y2 = 0 + -3y + 1y2
5y + y2 = -3y + 1y2

Solving
5y + y2 = -3y + 1y2

Solving for variable 'y'.

Reorder the terms:
5y + 3y + y2 + -1y2 = -3y + 1y2 + 3y + -1y2

Combine like terms: 5y + 3y = 8y
8y + y2 + -1y2 = -3y + 1y2 + 3y + -1y2

Combine like terms: y2 + -1y2 = 0
8y + 0 = -3y + 1y2 + 3y + -1y2
8y = -3y + 1y2 + 3y + -1y2

Reorder the terms:
8y = -3y + 3y + 1y2 + -1y2

Combine like terms: -3y + 3y = 0
8y = 0 + 1y2 + -1y2
8y = 1y2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
8y = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Solution
y = {0}

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