y^2-1y-1y+1=2y^2+8y+25

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Solution for y^2-1y-1y+1=2y^2+8y+25 equation: 


Simplifying
y2 + -1y + -1y + 1 = 2y2 + 8y + 25

Reorder the terms:
1 + -1y + -1y + y2 = 2y2 + 8y + 25

Combine like terms: -1y + -1y = -2y
1 + -2y + y2 = 2y2 + 8y + 25

Reorder the terms:
1 + -2y + y2 = 25 + 8y + 2y2

Solving
1 + -2y + y2 = 25 + 8y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + -25 + -2y + -8y + y2 + -2y2 = 25 + 8y + 2y2 + -25 + -8y + -2y2

Combine like terms: 1 + -25 = -24
-24 + -2y + -8y + y2 + -2y2 = 25 + 8y + 2y2 + -25 + -8y + -2y2

Combine like terms: -2y + -8y = -10y
-24 + -10y + y2 + -2y2 = 25 + 8y + 2y2 + -25 + -8y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-24 + -10y + -1y2 = 25 + 8y + 2y2 + -25 + -8y + -2y2

Reorder the terms:
-24 + -10y + -1y2 = 25 + -25 + 8y + -8y + 2y2 + -2y2

Combine like terms: 25 + -25 = 0
-24 + -10y + -1y2 = 0 + 8y + -8y + 2y2 + -2y2
-24 + -10y + -1y2 = 8y + -8y + 2y2 + -2y2

Combine like terms: 8y + -8y = 0
-24 + -10y + -1y2 = 0 + 2y2 + -2y2
-24 + -10y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-24 + -10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 10y + y2) = 0

Factor a trinomial.
-1((6 + y)(4 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6

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

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

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

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

Simplifying
y = -4
Solution
y = {-6, -4}

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