-7y=4y^2+3

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

Simplifying
-7y = 4y2 + 3

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

Solving
-7y = 3 + 4y2

Solving for variable 'y'.

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

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

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

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

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

Factor a trinomial.
-1((1 + y)(3 + 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 '(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}