-2y^2+14y=24

Solution for -2y^2+14y=24 equation:

Simplifying
-2y2 + 14y = 24

Reorder the terms:
14y + -2y2 = 24

Solving
14y + -2y2 = 24

Solving for variable 'y'.

Reorder the terms:
-24 + 14y + -2y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 14y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 7y + -1y2) = 0

Factor a trinomial.
2((-4 + y)(3 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 0

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

Add '4' to each side of the equation.
-4 + 4 + y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + y = 0 + 4
y = 0 + 4

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4
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 = {4, 3}