(3y-6)(y-6)=420

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Solution for (3y-6)(y-6)=420 equation: 


Simplifying
(3y + -6)(y + -6) = 420

Reorder the terms:
(-6 + 3y)(y + -6) = 420

Reorder the terms:
(-6 + 3y)(-6 + y) = 420

Multiply (-6 + 3y) * (-6 + y)
(-6(-6 + y) + 3y * (-6 + y)) = 420
((-6 * -6 + y * -6) + 3y * (-6 + y)) = 420
((36 + -6y) + 3y * (-6 + y)) = 420
(36 + -6y + (-6 * 3y + y * 3y)) = 420
(36 + -6y + (-18y + 3y2)) = 420

Combine like terms: -6y + -18y = -24y
(36 + -24y + 3y2) = 420

Solving
36 + -24y + 3y2 = 420

Solving for variable 'y'.

Reorder the terms:
36 + -420 + -24y + 3y2 = 420 + -420

Combine like terms: 36 + -420 = -384
-384 + -24y + 3y2 = 420 + -420

Combine like terms: 420 + -420 = 0
-384 + -24y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-128 + -8y + y2) = 0

Factor a trinomial.
3((-8 + -1y)(16 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

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

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

Divide each side by '-1'.
y = -8

Simplifying
y = -8

Subproblem 2
Set the factor '(16 + -1y)' equal to zero and attempt to solve:

Simplifying
16 + -1y = 0

Solving
16 + -1y = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1y = 0 + -16
-1y = 0 + -16

Combine like terms: 0 + -16 = -16
-1y = -16

Divide each side by '-1'.
y = 16

Simplifying
y = 16
Solution
y = {-8, 16}

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