4(y^2+10)-3y(y+4)=2(y-4)

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Solution for 4(y^2+10)-3y(y+4)=2(y-4) equation: 


Simplifying
4(y2 + 10) + -3y(y + 4) = 2(y + -4)

Reorder the terms:
4(10 + y2) + -3y(y + 4) = 2(y + -4)
(10 * 4 + y2 * 4) + -3y(y + 4) = 2(y + -4)
(40 + 4y2) + -3y(y + 4) = 2(y + -4)

Reorder the terms:
40 + 4y2 + -3y(4 + y) = 2(y + -4)
40 + 4y2 + (4 * -3y + y * -3y) = 2(y + -4)
40 + 4y2 + (-12y + -3y2) = 2(y + -4)

Reorder the terms:
40 + -12y + 4y2 + -3y2 = 2(y + -4)

Combine like terms: 4y2 + -3y2 = 1y2
40 + -12y + 1y2 = 2(y + -4)

Reorder the terms:
40 + -12y + 1y2 = 2(-4 + y)
40 + -12y + 1y2 = (-4 * 2 + y * 2)
40 + -12y + 1y2 = (-8 + 2y)

Solving
40 + -12y + 1y2 = -8 + 2y

Solving for variable 'y'.

Reorder the terms:
40 + 8 + -12y + -2y + 1y2 = -8 + 2y + 8 + -2y

Combine like terms: 40 + 8 = 48
48 + -12y + -2y + 1y2 = -8 + 2y + 8 + -2y

Combine like terms: -12y + -2y = -14y
48 + -14y + 1y2 = -8 + 2y + 8 + -2y

Reorder the terms:
48 + -14y + 1y2 = -8 + 8 + 2y + -2y

Combine like terms: -8 + 8 = 0
48 + -14y + 1y2 = 0 + 2y + -2y
48 + -14y + 1y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
48 + -14y + 1y2 = 0

Factor a trinomial.
(6 + -1y)(8 + -1y) = 0


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

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

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

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

Divide each side by '-1'.
y = 6

Simplifying
y = 6

Subproblem 2
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
Solution
y = {6, 8}

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