4y^2=14y-6

Solution for 4y^2=14y-6 equation:

Simplifying
4y2 = 14y + -6

Reorder the terms:
4y2 = -6 + 14y

Solving
4y2 = -6 + 14y

Solving for variable 'y'.

Reorder the terms:
6 + -14y + 4y2 = -6 + 14y + 6 + -14y

Reorder the terms:
6 + -14y + 4y2 = -6 + 6 + 14y + -14y

Combine like terms: -6 + 6 = 0
6 + -14y + 4y2 = 0 + 14y + -14y
6 + -14y + 4y2 = 14y + -14y

Combine like terms: 14y + -14y = 0
6 + -14y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7y + 2y2) = 0

Factor a trinomial.
2((1 + -2y)(3 + -1y)) = 0

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {0.5, 3}