y(3y+2)-2(y^2-8)=y(y+5)-6y+7

Solution for y(3y+2)-2(y^2-8)=y(y+5)-6y+7 equation:

Simplifying
y(3y + 2) + -2(y2 + -8) = y(y + 5) + -6y + 7

Reorder the terms:
y(2 + 3y) + -2(y2 + -8) = y(y + 5) + -6y + 7
(2 * y + 3y * y) + -2(y2 + -8) = y(y + 5) + -6y + 7
(2y + 3y2) + -2(y2 + -8) = y(y + 5) + -6y + 7

Reorder the terms:
2y + 3y2 + -2(-8 + y2) = y(y + 5) + -6y + 7
2y + 3y2 + (-8 * -2 + y2 * -2) = y(y + 5) + -6y + 7
2y + 3y2 + (16 + -2y2) = y(y + 5) + -6y + 7

Reorder the terms:
16 + 2y + 3y2 + -2y2 = y(y + 5) + -6y + 7

Combine like terms: 3y2 + -2y2 = 1y2
16 + 2y + 1y2 = y(y + 5) + -6y + 7

Reorder the terms:
16 + 2y + 1y2 = y(5 + y) + -6y + 7
16 + 2y + 1y2 = (5 * y + y * y) + -6y + 7
16 + 2y + 1y2 = (5y + y2) + -6y + 7

Reorder the terms:
16 + 2y + 1y2 = 7 + 5y + -6y + y2

Combine like terms: 5y + -6y = -1y
16 + 2y + 1y2 = 7 + -1y + y2

Solving
16 + 2y + 1y2 = 7 + -1y + y2

Solving for variable 'y'.

Reorder the terms:
16 + -7 + 2y + y + 1y2 + -1y2 = 7 + -1y + y2 + -7 + y + -1y2

Combine like terms: 16 + -7 = 9
9 + 2y + y + 1y2 + -1y2 = 7 + -1y + y2 + -7 + y + -1y2

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

Combine like terms: 1y2 + -1y2 = 0
9 + 3y + 0 = 7 + -1y + y2 + -7 + y + -1y2
9 + 3y = 7 + -1y + y2 + -7 + y + -1y2

Reorder the terms:
9 + 3y = 7 + -7 + -1y + y + y2 + -1y2

Combine like terms: 7 + -7 = 0
9 + 3y = 0 + -1y + y + y2 + -1y2
9 + 3y = -1y + y + y2 + -1y2

Combine like terms: -1y + y = 0
9 + 3y = 0 + y2 + -1y2
9 + 3y = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
9 + 3y = 0

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

Ignore the factor 3.
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
Solution
y = {-3}