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

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

Simplifying
1(1 + y) = 5 + -3y2
(1 * 1 + y * 1) = 5 + -3y2
(1 + 1y) = 5 + -3y2

Solving
1 + 1y = 5 + -3y2

Solving for variable 'y'.

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

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

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

Combine like terms: 5 + -5 = 0
-4 + 1y + 3y2 = 0 + -3y2 + 3y2
-4 + 1y + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-4 + 1y + 3y2 = 0

Factor a trinomial.
(-4 + -3y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y = 0 + 4
-3y = 0 + 4

Combine like terms: 0 + 4 = 4
-3y = 4

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-1.333333333, 1}