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

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


Simplifying
(y + -7)(y + 4) = y + -7

Reorder the terms:
(-7 + y)(y + 4) = y + -7

Reorder the terms:
(-7 + y)(4 + y) = y + -7

Multiply (-7 + y) * (4 + y)
(-7(4 + y) + y(4 + y)) = y + -7
((4 * -7 + y * -7) + y(4 + y)) = y + -7
((-28 + -7y) + y(4 + y)) = y + -7
(-28 + -7y + (4 * y + y * y)) = y + -7
(-28 + -7y + (4y + y2)) = y + -7

Combine like terms: -7y + 4y = -3y
(-28 + -3y + y2) = y + -7

Reorder the terms:
-28 + -3y + y2 = -7 + y

Solving
-28 + -3y + y2 = -7 + y

Solving for variable 'y'.

Reorder the terms:
-28 + 7 + -3y + -1y + y2 = -7 + y + 7 + -1y

Combine like terms: -28 + 7 = -21
-21 + -3y + -1y + y2 = -7 + y + 7 + -1y

Combine like terms: -3y + -1y = -4y
-21 + -4y + y2 = -7 + y + 7 + -1y

Reorder the terms:
-21 + -4y + y2 = -7 + 7 + y + -1y

Combine like terms: -7 + 7 = 0
-21 + -4y + y2 = 0 + y + -1y
-21 + -4y + y2 = y + -1y

Combine like terms: y + -1y = 0
-21 + -4y + y2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

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

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