3(y+1)(y+1)-5=43

Solution for 3(y+1)(y+1)-5=43 equation:

Simplifying
3(y + 1)(y + 1) + -5 = 43

Reorder the terms:
3(1 + y)(y + 1) + -5 = 43

Reorder the terms:
3(1 + y)(1 + y) + -5 = 43

Multiply (1 + y) * (1 + y)
3(1(1 + y) + y(1 + y)) + -5 = 43
3((1 * 1 + y * 1) + y(1 + y)) + -5 = 43
3((1 + 1y) + y(1 + y)) + -5 = 43
3(1 + 1y + (1 * y + y * y)) + -5 = 43
3(1 + 1y + (1y + y2)) + -5 = 43

Combine like terms: 1y + 1y = 2y
3(1 + 2y + y2) + -5 = 43
(1 * 3 + 2y * 3 + y2 * 3) + -5 = 43
(3 + 6y + 3y2) + -5 = 43

Reorder the terms:
3 + -5 + 6y + 3y2 = 43

Combine like terms: 3 + -5 = -2
-2 + 6y + 3y2 = 43

Solving
-2 + 6y + 3y2 = 43

Solving for variable 'y'.

Reorder the terms:
-2 + -43 + 6y + 3y2 = 43 + -43

Combine like terms: -2 + -43 = -45
-45 + 6y + 3y2 = 43 + -43

Combine like terms: 43 + -43 = 0
-45 + 6y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2y + y2) = 0

Factor a trinomial.
3((-5 + -1y)(3 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-5, 3}