6(y-2)+1(y+2)=(y+2)(y-2)

Solution for 6(y-2)+1(y+2)=(y+2)(y-2) equation:

Simplifying
6(y + -2) + 1(y + 2) = (y + 2)(y + -2)

Reorder the terms:
6(-2 + y) + 1(y + 2) = (y + 2)(y + -2)
(-2 * 6 + y * 6) + 1(y + 2) = (y + 2)(y + -2)
(-12 + 6y) + 1(y + 2) = (y + 2)(y + -2)

Reorder the terms:
-12 + 6y + 1(2 + y) = (y + 2)(y + -2)
-12 + 6y + (2 * 1 + y * 1) = (y + 2)(y + -2)
-12 + 6y + (2 + 1y) = (y + 2)(y + -2)

Reorder the terms:
-12 + 2 + 6y + 1y = (y + 2)(y + -2)

Combine like terms: -12 + 2 = -10
-10 + 6y + 1y = (y + 2)(y + -2)

Combine like terms: 6y + 1y = 7y
-10 + 7y = (y + 2)(y + -2)

Reorder the terms:
-10 + 7y = (2 + y)(y + -2)

Reorder the terms:
-10 + 7y = (2 + y)(-2 + y)

Multiply (2 + y) * (-2 + y)
-10 + 7y = (2(-2 + y) + y(-2 + y))
-10 + 7y = ((-2 * 2 + y * 2) + y(-2 + y))
-10 + 7y = ((-4 + 2y) + y(-2 + y))
-10 + 7y = (-4 + 2y + (-2 * y + y * y))
-10 + 7y = (-4 + 2y + (-2y + y2))

Combine like terms: 2y + -2y = 0
-10 + 7y = (-4 + 0 + y2)
-10 + 7y = (-4 + y2)

Solving
-10 + 7y = -4 + y2

Solving for variable 'y'.

Reorder the terms:
-10 + 4 + 7y + -1y2 = -4 + y2 + 4 + -1y2

Combine like terms: -10 + 4 = -6
-6 + 7y + -1y2 = -4 + y2 + 4 + -1y2

Reorder the terms:
-6 + 7y + -1y2 = -4 + 4 + y2 + -1y2

Combine like terms: -4 + 4 = 0
-6 + 7y + -1y2 = 0 + y2 + -1y2
-6 + 7y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-6 + 7y + -1y2 = 0

Factor a trinomial.
(-6 + y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Subproblem 2
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
Solution
y = {6, 1}