9y(y-2)+4=31

Solution for 9y(y-2)+4=31 equation:

Simplifying
9y(y + -2) + 4 = 31

Reorder the terms:
9y(-2 + y) + 4 = 31
(-2 * 9y + y * 9y) + 4 = 31
(-18y + 9y2) + 4 = 31

Reorder the terms:
4 + -18y + 9y2 = 31

Solving
4 + -18y + 9y2 = 31

Solving for variable 'y'.

Reorder the terms:
4 + -31 + -18y + 9y2 = 31 + -31

Combine like terms: 4 + -31 = -27
-27 + -18y + 9y2 = 31 + -31

Combine like terms: 31 + -31 = 0
-27 + -18y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + -2y + y2) = 0

Factor a trinomial.
9((-1 + -1y)(3 + -1y)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y = 0 + 1
-1y = 0 + 1

Combine like terms: 0 + 1 = 1
-1y = 1

Divide each side by '-1'.
y = -1

Simplifying
y = -1
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 = {-1, 3}