-4y^2-3y+3=2y+4

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

Simplifying
-4y2 + -3y + 3 = 2y + 4

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

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

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

Solving for variable 'y'.

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

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

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

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

Combine like terms: 4 + -4 = 0
-1 + -5y + -4y2 = 0 + 2y + -2y
-1 + -5y + -4y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-1 + -5y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 5y + 4y2) = 0

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

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 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 + 4y = 0 + -1

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

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

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {-1, -0.25}