4y(y-3)=16

Solution for 4y(y-3)=16 equation:

Simplifying
4y(y + -3) = 16

Reorder the terms:
4y(-3 + y) = 16
(-3 * 4y + y * 4y) = 16
(-12y + 4y2) = 16

Solving
-12y + 4y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -12y + 4y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -12y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -3y + y2) = 0

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

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

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-1, 4}