4y=7y^2-3

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

Simplifying
4y = 7y2 + -3

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

Solving
4y = -3 + 7y2

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(1 + -1y)(3 + 7y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 7y)' equal to zero and attempt to solve:

Simplifying
3 + 7y = 0

Solving
3 + 7y = 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 + 7y = 0 + -3

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

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

Divide each side by '7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
Solution
y = {1, -0.4285714286}