y^2+10y+25=2y^2+20y+46

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Solution for y^2+10y+25=2y^2+20y+46 equation: 


Simplifying
y2 + 10y + 25 = 2y2 + 20y + 46

Reorder the terms:
25 + 10y + y2 = 2y2 + 20y + 46

Reorder the terms:
25 + 10y + y2 = 46 + 20y + 2y2

Solving
25 + 10y + y2 = 46 + 20y + 2y2

Solving for variable 'y'.

Reorder the terms:
25 + -46 + 10y + -20y + y2 + -2y2 = 46 + 20y + 2y2 + -46 + -20y + -2y2

Combine like terms: 25 + -46 = -21
-21 + 10y + -20y + y2 + -2y2 = 46 + 20y + 2y2 + -46 + -20y + -2y2

Combine like terms: 10y + -20y = -10y
-21 + -10y + y2 + -2y2 = 46 + 20y + 2y2 + -46 + -20y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-21 + -10y + -1y2 = 46 + 20y + 2y2 + -46 + -20y + -2y2

Reorder the terms:
-21 + -10y + -1y2 = 46 + -46 + 20y + -20y + 2y2 + -2y2

Combine like terms: 46 + -46 = 0
-21 + -10y + -1y2 = 0 + 20y + -20y + 2y2 + -2y2
-21 + -10y + -1y2 = 20y + -20y + 2y2 + -2y2

Combine like terms: 20y + -20y = 0
-21 + -10y + -1y2 = 0 + 2y2 + -2y2
-21 + -10y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-21 + -10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10y + y2) = 0

Factor a trinomial.
-1((7 + y)(3 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

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

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

Simplifying
y = -3
Solution
y = {-7, -3}

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