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

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

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

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

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

Multiply 2 * 5
10(-1 + y) = 4(y + -3) * y
(-1 * 10 + y * 10) = 4(y + -3) * y
(-10 + 10y) = 4(y + -3) * y

Reorder the terms:
-10 + 10y = 4(-3 + y) * y

Reorder the terms for easier multiplication:
-10 + 10y = 4y(-3 + y)
-10 + 10y = (-3 * 4y + y * 4y)
-10 + 10y = (-12y + 4y2)

Solving
-10 + 10y = -12y + 4y2

Solving for variable 'y'.

Combine like terms: 10y + 12y = 22y
-10 + 22y + -4y2 = -12y + 4y2 + 12y + -4y2

Reorder the terms:
-10 + 22y + -4y2 = -12y + 12y + 4y2 + -4y2

Combine like terms: -12y + 12y = 0
-10 + 22y + -4y2 = 0 + 4y2 + -4y2
-10 + 22y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-10 + 22y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 11y + -2y2) = 0

Factor a trinomial.
2((-5 + y)(1 + -2y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {5, 0.5}