-7y^2+42y-63=0

Solution for -7y^2+42y-63=0 equation:

Simplifying
-7y2 + 42y + -63 = 0

Reorder the terms:
-63 + 42y + -7y2 = 0

Solving
-63 + 42y + -7y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-9 + 6y + -1y2) = 0

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

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

Simplifying
-3 + y = 0

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

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

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

Simplifying
y = 3
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 = {3, 3}