6(y-4)=y^2-16

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Solution for 6(y-4)=y^2-16 equation: 


Simplifying
6(y + -4) = y2 + -16

Reorder the terms:
6(-4 + y) = y2 + -16
(-4 * 6 + y * 6) = y2 + -16
(-24 + 6y) = y2 + -16

Reorder the terms:
-24 + 6y = -16 + y2

Solving
-24 + 6y = -16 + y2

Solving for variable 'y'.

Reorder the terms:
-24 + 16 + 6y + -1y2 = -16 + y2 + 16 + -1y2

Combine like terms: -24 + 16 = -8
-8 + 6y + -1y2 = -16 + y2 + 16 + -1y2

Reorder the terms:
-8 + 6y + -1y2 = -16 + 16 + y2 + -1y2

Combine like terms: -16 + 16 = 0
-8 + 6y + -1y2 = 0 + y2 + -1y2
-8 + 6y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-8 + 6y + -1y2 = 0

Factor a trinomial.
(-4 + y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 0

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

Add '4' to each side of the equation.
-4 + 4 + y = 0 + 4

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

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {4, 2}

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