12y^2-21y+16=1

Solution for 12y^2-21y+16=1 equation:

Simplifying
12y2 + -21y + 16 = 1

Reorder the terms:
16 + -21y + 12y2 = 1

Solving
16 + -21y + 12y2 = 1

Solving for variable 'y'.

Reorder the terms:
16 + -1 + -21y + 12y2 = 1 + -1

Combine like terms: 16 + -1 = 15
15 + -21y + 12y2 = 1 + -1

Combine like terms: 1 + -1 = 0
15 + -21y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -7y + 4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -7y + 4y2)' equal to zero and attempt to solve:

Simplifying
5 + -7y + 4y2 = 0

Solving
5 + -7y + 4y2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1.25 + -1.75y + y2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -1.75y + -1.25 + y2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -1.75y + y2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -1.75y + y2 = 0 + -1.25
-1.75y + y2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-1.75y + y2 = -1.25

The y term is -1.75y.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75y + 0.765625 + y2 = -1.25 + 0.765625

Reorder the terms:
0.765625 + -1.75y + y2 = -1.25 + 0.765625

Combine like terms: -1.25 + 0.765625 = -0.484375
0.765625 + -1.75y + y2 = -0.484375

Factor a perfect square on the left side:
(y + -0.875)(y + -0.875) = -0.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.