4y^2-10y+42=0

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Solution for 4y^2-10y+42=0 equation: 


Simplifying
4y2 + -10y + 42 = 0

Reorder the terms:
42 + -10y + 4y2 = 0

Solving
42 + -10y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -5y + 2y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(21 + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
21 + -5y + 2y2 = 0

Solving
21 + -5y + 2y2 = 0

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

Divide each side by '2'.
10.5 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -2.5y + -10.5 + y2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -2.5y + y2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -2.5y + y2 = 0 + -10.5
-2.5y + y2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-2.5y + y2 = -10.5

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = -10.5 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -10.5 + 1.5625

Combine like terms: -10.5 + 1.5625 = -8.9375
1.5625 + -2.5y + y2 = -8.9375

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = -8.9375

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.

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