21y^2-125y=-34

Solution for 21y^2-125y=-34 equation:

Simplifying
21y2 + -125y = -34

Reorder the terms:
-125y + 21y2 = -34

Solving
-125y + 21y2 = -34

Solving for variable 'y'.

Reorder the terms:
34 + -125y + 21y2 = -34 + 34

Combine like terms: -34 + 34 = 0
34 + -125y + 21y2 = 0

Factor a trinomial.
(2 + -7y)(17 + -3y) = 0

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

Simplifying
2 + -7y = 0

Solving
2 + -7y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -7y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7y = 0 + -2
-7y = 0 + -2

Combine like terms: 0 + -2 = -2
-7y = -2

Divide each side by '-7'.
y = 0.2857142857

Simplifying
y = 0.2857142857
Subproblem 2
Set the factor '(17 + -3y)' equal to zero and attempt to solve:

Simplifying
17 + -3y = 0

Solving
17 + -3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + -3y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3y = 0 + -17
-3y = 0 + -17

Combine like terms: 0 + -17 = -17
-3y = -17

Divide each side by '-3'.
y = 5.666666667

Simplifying
y = 5.666666667
Solution
y = {0.2857142857, 5.666666667}