2y^2-2y-12=(y-3)(y-3)

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Solution for 2y^2-2y-12=(y-3)(y-3) equation: 


Simplifying
2y2 + -2y + -12 = (y + -3)(y + -3)

Reorder the terms:
-12 + -2y + 2y2 = (y + -3)(y + -3)

Reorder the terms:
-12 + -2y + 2y2 = (-3 + y)(y + -3)

Reorder the terms:
-12 + -2y + 2y2 = (-3 + y)(-3 + y)

Multiply (-3 + y) * (-3 + y)
-12 + -2y + 2y2 = (-3(-3 + y) + y(-3 + y))
-12 + -2y + 2y2 = ((-3 * -3 + y * -3) + y(-3 + y))
-12 + -2y + 2y2 = ((9 + -3y) + y(-3 + y))
-12 + -2y + 2y2 = (9 + -3y + (-3 * y + y * y))
-12 + -2y + 2y2 = (9 + -3y + (-3y + y2))

Combine like terms: -3y + -3y = -6y
-12 + -2y + 2y2 = (9 + -6y + y2)

Solving
-12 + -2y + 2y2 = 9 + -6y + y2

Solving for variable 'y'.

Reorder the terms:
-12 + -9 + -2y + 6y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2

Combine like terms: -12 + -9 = -21
-21 + -2y + 6y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2

Combine like terms: -2y + 6y = 4y
-21 + 4y + 2y2 + -1y2 = 9 + -6y + y2 + -9 + 6y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-21 + 4y + 1y2 = 9 + -6y + y2 + -9 + 6y + -1y2

Reorder the terms:
-21 + 4y + 1y2 = 9 + -9 + -6y + 6y + y2 + -1y2

Combine like terms: 9 + -9 = 0
-21 + 4y + 1y2 = 0 + -6y + 6y + y2 + -1y2
-21 + 4y + 1y2 = -6y + 6y + y2 + -1y2

Combine like terms: -6y + 6y = 0
-21 + 4y + 1y2 = 0 + y2 + -1y2
-21 + 4y + 1y2 = y2 + -1y2

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

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


Subproblem 1
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

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 = {-7, 3}

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