(y+4)(3y-2)=-y-14

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Solution for (y+4)(3y-2)=-y-14 equation: 


Simplifying
(y + 4)(3y + -2) = -1y + -14

Reorder the terms:
(4 + y)(3y + -2) = -1y + -14

Reorder the terms:
(4 + y)(-2 + 3y) = -1y + -14

Multiply (4 + y) * (-2 + 3y)
(4(-2 + 3y) + y(-2 + 3y)) = -1y + -14
((-2 * 4 + 3y * 4) + y(-2 + 3y)) = -1y + -14
((-8 + 12y) + y(-2 + 3y)) = -1y + -14
(-8 + 12y + (-2 * y + 3y * y)) = -1y + -14
(-8 + 12y + (-2y + 3y2)) = -1y + -14

Combine like terms: 12y + -2y = 10y
(-8 + 10y + 3y2) = -1y + -14

Reorder the terms:
-8 + 10y + 3y2 = -14 + -1y

Solving
-8 + 10y + 3y2 = -14 + -1y

Solving for variable 'y'.

Reorder the terms:
-8 + 14 + 10y + y + 3y2 = -14 + -1y + 14 + y

Combine like terms: -8 + 14 = 6
6 + 10y + y + 3y2 = -14 + -1y + 14 + y

Combine like terms: 10y + y = 11y
6 + 11y + 3y2 = -14 + -1y + 14 + y

Reorder the terms:
6 + 11y + 3y2 = -14 + 14 + -1y + y

Combine like terms: -14 + 14 = 0
6 + 11y + 3y2 = 0 + -1y + y
6 + 11y + 3y2 = -1y + y

Combine like terms: -1y + y = 0
6 + 11y + 3y2 = 0

Factor a trinomial.
(3 + y)(2 + 3y) = 0


Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3

Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-3, -0.6666666667}

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