(3y+4)(y+1)=2y^2+y-5

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Solution for (3y+4)(y+1)=2y^2+y-5 equation: 


Simplifying
(3y + 4)(y + 1) = 2y2 + y + -5

Reorder the terms:
(4 + 3y)(y + 1) = 2y2 + y + -5

Reorder the terms:
(4 + 3y)(1 + y) = 2y2 + y + -5

Multiply (4 + 3y) * (1 + y)
(4(1 + y) + 3y * (1 + y)) = 2y2 + y + -5
((1 * 4 + y * 4) + 3y * (1 + y)) = 2y2 + y + -5
((4 + 4y) + 3y * (1 + y)) = 2y2 + y + -5
(4 + 4y + (1 * 3y + y * 3y)) = 2y2 + y + -5
(4 + 4y + (3y + 3y2)) = 2y2 + y + -5

Combine like terms: 4y + 3y = 7y
(4 + 7y + 3y2) = 2y2 + y + -5

Reorder the terms:
4 + 7y + 3y2 = -5 + y + 2y2

Solving
4 + 7y + 3y2 = -5 + y + 2y2

Solving for variable 'y'.

Reorder the terms:
4 + 5 + 7y + -1y + 3y2 + -2y2 = -5 + y + 2y2 + 5 + -1y + -2y2

Combine like terms: 4 + 5 = 9
9 + 7y + -1y + 3y2 + -2y2 = -5 + y + 2y2 + 5 + -1y + -2y2

Combine like terms: 7y + -1y = 6y
9 + 6y + 3y2 + -2y2 = -5 + y + 2y2 + 5 + -1y + -2y2

Combine like terms: 3y2 + -2y2 = 1y2
9 + 6y + 1y2 = -5 + y + 2y2 + 5 + -1y + -2y2

Reorder the terms:
9 + 6y + 1y2 = -5 + 5 + y + -1y + 2y2 + -2y2

Combine like terms: -5 + 5 = 0
9 + 6y + 1y2 = 0 + y + -1y + 2y2 + -2y2
9 + 6y + 1y2 = y + -1y + 2y2 + -2y2

Combine like terms: y + -1y = 0
9 + 6y + 1y2 = 0 + 2y2 + -2y2
9 + 6y + 1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
9 + 6y + 1y2 = 0

Factor a trinomial.
(3 + y)(3 + y) = 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 '(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
Solution
y = {-3, -3}

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