2(y-22)3(y-4)=24

Solution for 2(y-22)3(y-4)=24 equation:

Simplifying
2(y + -22) * 3(y + -4) = 24

Reorder the terms:
2(-22 + y) * 3(y + -4) = 24

Reorder the terms:
2(-22 + y) * 3(-4 + y) = 24

Reorder the terms for easier multiplication:
2 * 3(-22 + y)(-4 + y) = 24

Multiply 2 * 3
6(-22 + y)(-4 + y) = 24

Multiply (-22 + y) * (-4 + y)
6(-22(-4 + y) + y(-4 + y)) = 24
6((-4 * -22 + y * -22) + y(-4 + y)) = 24
6((88 + -22y) + y(-4 + y)) = 24
6(88 + -22y + (-4 * y + y * y)) = 24
6(88 + -22y + (-4y + y2)) = 24

Combine like terms: -22y + -4y = -26y
6(88 + -26y + y2) = 24
(88 * 6 + -26y * 6 + y2 * 6) = 24
(528 + -156y + 6y2) = 24

Solving
528 + -156y + 6y2 = 24

Solving for variable 'y'.

Reorder the terms:
528 + -24 + -156y + 6y2 = 24 + -24

Combine like terms: 528 + -24 = 504
504 + -156y + 6y2 = 24 + -24

Combine like terms: 24 + -24 = 0
504 + -156y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(84 + -26y + y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(84 + -26y + y2)' equal to zero and attempt to solve:

Simplifying
84 + -26y + y2 = 0

Solving
84 + -26y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-84' to each side of the equation.
84 + -26y + -84 + y2 = 0 + -84

Reorder the terms:
84 + -84 + -26y + y2 = 0 + -84

Combine like terms: 84 + -84 = 0
0 + -26y + y2 = 0 + -84
-26y + y2 = 0 + -84

Combine like terms: 0 + -84 = -84
-26y + y2 = -84

The y term is -26y.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26y + 169 + y2 = -84 + 169

Reorder the terms:
169 + -26y + y2 = -84 + 169

Combine like terms: -84 + 169 = 85
169 + -26y + y2 = 85

Factor a perfect square on the left side:
(y + -13)(y + -13) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(y + -13) equal to 9.219544457 and -9.219544457.

Subproblem 1
y + -13 = 9.219544457

Simplifying
y + -13 = 9.219544457

Reorder the terms:
-13 + y = 9.219544457

Solving
-13 + y = 9.219544457

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = 9.219544457 + 13

Combine like terms: -13 + 13 = 0
0 + y = 9.219544457 + 13
y = 9.219544457 + 13

Combine like terms: 9.219544457 + 13 = 22.219544457
y = 22.219544457

Simplifying
y = 22.219544457

Subproblem 2
y + -13 = -9.219544457

Simplifying
y + -13 = -9.219544457

Reorder the terms:
-13 + y = -9.219544457

Solving
-13 + y = -9.219544457

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = -9.219544457 + 13

Combine like terms: -13 + 13 = 0
0 + y = -9.219544457 + 13
y = -9.219544457 + 13

Combine like terms: -9.219544457 + 13 = 3.780455543
y = 3.780455543

Simplifying
y = 3.780455543

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {22.219544457, 3.780455543}
Solution
y = {22.219544457, 3.780455543}