y(y-7)=-10

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

Simplifying
y(y + -7) = -10

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

Solving
-7y + y2 = -10

Solving for variable 'y'.

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

Combine like terms: -10 + 10 = 0
10 + -7y + 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}