y(y-7)=2(5-2y)

Solution for y(y-7)=2(5-2y) equation:

Simplifying
y(y + -7) = 2(5 + -2y)

Reorder the terms:
y(-7 + y) = 2(5 + -2y)
(-7 * y + y * y) = 2(5 + -2y)
(-7y + y2) = 2(5 + -2y)
-7y + y2 = (5 * 2 + -2y * 2)
-7y + y2 = (10 + -4y)

Solving
-7y + y2 = 10 + -4y

Solving for variable 'y'.

Reorder the terms:
-10 + -7y + 4y + y2 = 10 + -4y + -10 + 4y

Combine like terms: -7y + 4y = -3y
-10 + -3y + y2 = 10 + -4y + -10 + 4y

Reorder the terms:
-10 + -3y + y2 = 10 + -10 + -4y + 4y

Combine like terms: 10 + -10 = 0
-10 + -3y + y2 = 0 + -4y + 4y
-10 + -3y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-10 + -3y + y2 = 0

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

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-2, 5}