4(y-1)3y=9y-(5+2y)+1

Solution for 4(y-1)3y=9y-(5+2y)+1 equation:

Simplifying
4(y + -1) * 3y = 9y + -1(5 + 2y) + 1

Reorder the terms:
4(-1 + y) * 3y = 9y + -1(5 + 2y) + 1

Reorder the terms for easier multiplication:
4 * 3y(-1 + y) = 9y + -1(5 + 2y) + 1

Multiply 4 * 3
12y(-1 + y) = 9y + -1(5 + 2y) + 1
(-1 * 12y + y * 12y) = 9y + -1(5 + 2y) + 1
(-12y + 12y2) = 9y + -1(5 + 2y) + 1
-12y + 12y2 = 9y + (5 * -1 + 2y * -1) + 1
-12y + 12y2 = 9y + (-5 + -2y) + 1

Reorder the terms:
-12y + 12y2 = -5 + 1 + 9y + -2y

Combine like terms: -5 + 1 = -4
-12y + 12y2 = -4 + 9y + -2y

Combine like terms: 9y + -2y = 7y
-12y + 12y2 = -4 + 7y

Solving
-12y + 12y2 = -4 + 7y

Solving for variable 'y'.

Reorder the terms:
4 + -12y + -7y + 12y2 = -4 + 7y + 4 + -7y

Combine like terms: -12y + -7y = -19y
4 + -19y + 12y2 = -4 + 7y + 4 + -7y

Reorder the terms:
4 + -19y + 12y2 = -4 + 4 + 7y + -7y

Combine like terms: -4 + 4 = 0
4 + -19y + 12y2 = 0 + 7y + -7y
4 + -19y + 12y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
4 + -19y + 12y2 = 0

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

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

Simplifying
1 + -4y = 0

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

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

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

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Subproblem 2
Set the factor '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 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 + -3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3y = 0 + -4
-3y = 0 + -4

Combine like terms: 0 + -4 = -4
-3y = -4

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333
Solution
y = {0.25, 1.333333333}