4y^2=-7y-3

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

Simplifying
4y2 = -7y + -3

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

Solving
4y2 = -3 + -7y

Solving for variable 'y'.

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

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

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

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

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

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 '(3 + 4y)' equal to zero and attempt to solve:

Simplifying
3 + 4y = 0

Solving
3 + 4y = 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 + 4y = 0 + -3

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

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

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {-1, -0.75}