y^2+3y-7=6y+3

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Solution for y^2+3y-7=6y+3 equation: 


Simplifying
y2 + 3y + -7 = 6y + 3

Reorder the terms:
-7 + 3y + y2 = 6y + 3

Reorder the terms:
-7 + 3y + y2 = 3 + 6y

Solving
-7 + 3y + y2 = 3 + 6y

Solving for variable 'y'.

Reorder the terms:
-7 + -3 + 3y + -6y + y2 = 3 + 6y + -3 + -6y

Combine like terms: -7 + -3 = -10
-10 + 3y + -6y + y2 = 3 + 6y + -3 + -6y

Combine like terms: 3y + -6y = -3y
-10 + -3y + y2 = 3 + 6y + -3 + -6y

Reorder the terms:
-10 + -3y + y2 = 3 + -3 + 6y + -6y

Combine like terms: 3 + -3 = 0
-10 + -3y + y2 = 0 + 6y + -6y
-10 + -3y + y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-10 + -3y + y2 = 0

Factor a trinomial.
(-2 + -1y)(5 + -1y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2

Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-2, 5}

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