4+y+y^2=7-y(2-y)

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Solution for 4+y+y^2=7-y(2-y) equation: 


Simplifying
4 + y + y2 = 7 + -1y(2 + -1y)
4 + y + y2 = 7 + (2 * -1y + -1y * -1y)
4 + y + y2 = 7 + (-2y + 1y2)

Solving
4 + y + y2 = 7 + -2y + 1y2

Solving for variable 'y'.

Reorder the terms:
4 + -7 + y + 2y + y2 + -1y2 = 7 + -2y + 1y2 + -7 + 2y + -1y2

Combine like terms: 4 + -7 = -3
-3 + y + 2y + y2 + -1y2 = 7 + -2y + 1y2 + -7 + 2y + -1y2

Combine like terms: y + 2y = 3y
-3 + 3y + y2 + -1y2 = 7 + -2y + 1y2 + -7 + 2y + -1y2

Combine like terms: y2 + -1y2 = 0
-3 + 3y + 0 = 7 + -2y + 1y2 + -7 + 2y + -1y2
-3 + 3y = 7 + -2y + 1y2 + -7 + 2y + -1y2

Reorder the terms:
-3 + 3y = 7 + -7 + -2y + 2y + 1y2 + -1y2

Combine like terms: 7 + -7 = 0
-3 + 3y = 0 + -2y + 2y + 1y2 + -1y2
-3 + 3y = -2y + 2y + 1y2 + -1y2

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + y) = 0

Ignore the factor 3.

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

Simplifying
-1 + y = 0

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

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

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

Simplifying
y = 1
Solution
y = {1}

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