y-(2y-7)y=-10

Solution for y-(2y-7)y=-10 equation:

Simplifying
y + -1(2y + -7) * y = -10

Reorder the terms:
y + -1(-7 + 2y) * y = -10

Reorder the terms for easier multiplication:
y + -1y(-7 + 2y) = -10
y + (-7 * -1y + 2y * -1y) = -10
y + (7y + -2y2) = -10

Combine like terms: y + 7y = 8y
8y + -2y2 = -10

Solving
8y + -2y2 = -10

Solving for variable 'y'.

Reorder the terms:
10 + 8y + -2y2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 8y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4y + -1y2) = 0

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

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

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {5, -1}