-7y=3y^2+4

Solution for -7y=3y^2+4 equation:

Simplifying
-7y = 3y2 + 4

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

Solving
-7y = 4 + 3y2

Solving for variable 'y'.

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

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

Combine like terms: 4 + -4 = 0
-4 + -7y + -3y2 = 0 + 3y2 + -3y2
-4 + -7y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-4 + -7y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 7y + 3y2) = 0

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

Ignore the factor -1.
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 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

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