(y-3)(y+7)=(y-3)(y+3)

Solution for (y-3)(y+7)=(y-3)(y+3) equation:

Simplifying
(y + -3)(y + 7) = (y + -3)(y + 3)

Reorder the terms:
(-3 + y)(y + 7) = (y + -3)(y + 3)

Reorder the terms:
(-3 + y)(7 + y) = (y + -3)(y + 3)

Multiply (-3 + y) * (7 + y)
(-3(7 + y) + y(7 + y)) = (y + -3)(y + 3)
((7 * -3 + y * -3) + y(7 + y)) = (y + -3)(y + 3)
((-21 + -3y) + y(7 + y)) = (y + -3)(y + 3)
(-21 + -3y + (7 * y + y * y)) = (y + -3)(y + 3)
(-21 + -3y + (7y + y2)) = (y + -3)(y + 3)

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

Reorder the terms:
-21 + 4y + y2 = (-3 + y)(y + 3)

Reorder the terms:
-21 + 4y + y2 = (-3 + y)(3 + y)

Multiply (-3 + y) * (3 + y)
-21 + 4y + y2 = (-3(3 + y) + y(3 + y))
-21 + 4y + y2 = ((3 * -3 + y * -3) + y(3 + y))
-21 + 4y + y2 = ((-9 + -3y) + y(3 + y))
-21 + 4y + y2 = (-9 + -3y + (3 * y + y * y))
-21 + 4y + y2 = (-9 + -3y + (3y + y2))

Combine like terms: -3y + 3y = 0
-21 + 4y + y2 = (-9 + 0 + y2)
-21 + 4y + y2 = (-9 + y2)

Add '-1y2' to each side of the equation.
-21 + 4y + y2 + -1y2 = -9 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-21 + 4y + 0 = -9 + y2 + -1y2
-21 + 4y = -9 + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-21 + 4y = -9 + 0
-21 + 4y = -9

Solving
-21 + 4y = -9

Solving for variable 'y'.

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

Add '21' to each side of the equation.
-21 + 21 + 4y = -9 + 21

Combine like terms: -21 + 21 = 0
0 + 4y = -9 + 21
4y = -9 + 21

Combine like terms: -9 + 21 = 12
4y = 12

Divide each side by '4'.
y = 3

Simplifying
y = 3