(y-2)(y-2)+14=8y-3y

Solution for (y-2)(y-2)+14=8y-3y equation:

Simplifying
(y + -2)(y + -2) + 14 = 8y + -3y

Reorder the terms:
(-2 + y)(y + -2) + 14 = 8y + -3y

Reorder the terms:
(-2 + y)(-2 + y) + 14 = 8y + -3y

Multiply (-2 + y) * (-2 + y)
(-2(-2 + y) + y(-2 + y)) + 14 = 8y + -3y
((-2 * -2 + y * -2) + y(-2 + y)) + 14 = 8y + -3y
((4 + -2y) + y(-2 + y)) + 14 = 8y + -3y
(4 + -2y + (-2 * y + y * y)) + 14 = 8y + -3y
(4 + -2y + (-2y + y2)) + 14 = 8y + -3y

Combine like terms: -2y + -2y = -4y
(4 + -4y + y2) + 14 = 8y + -3y

Reorder the terms:
4 + 14 + -4y + y2 = 8y + -3y

Combine like terms: 4 + 14 = 18
18 + -4y + y2 = 8y + -3y

Combine like terms: 8y + -3y = 5y
18 + -4y + y2 = 5y

Solving
18 + -4y + y2 = 5y

Solving for variable 'y'.

Reorder the terms:
18 + -4y + -5y + y2 = 5y + -5y

Combine like terms: -4y + -5y = -9y
18 + -9y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
18 + -9y + y2 = 0

Factor a trinomial.
(3 + -1y)(6 + -1y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {3, 6}