y^2+3y-7=5y-4

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Solution for y^2+3y-7=5y-4 equation: 


Simplifying
y2 + 3y + -7 = 5y + -4

Reorder the terms:
-7 + 3y + y2 = 5y + -4

Reorder the terms:
-7 + 3y + y2 = -4 + 5y

Solving
-7 + 3y + y2 = -4 + 5y

Solving for variable 'y'.

Reorder the terms:
-7 + 4 + 3y + -5y + y2 = -4 + 5y + 4 + -5y

Combine like terms: -7 + 4 = -3
-3 + 3y + -5y + y2 = -4 + 5y + 4 + -5y

Combine like terms: 3y + -5y = -2y
-3 + -2y + y2 = -4 + 5y + 4 + -5y

Reorder the terms:
-3 + -2y + y2 = -4 + 4 + 5y + -5y

Combine like terms: -4 + 4 = 0
-3 + -2y + y2 = 0 + 5y + -5y
-3 + -2y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-3 + -2y + y2 = 0

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


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

Simplifying
-1 + -1y = 0

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

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

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

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

Simplifying
y = -1

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1, 3}

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