7y-10=-4+y^2

Solution for 7y-10=-4+y^2 equation:

Simplifying
7y + -10 = -4 + y2

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

Solving
-10 + 7y = -4 + y2

Solving for variable 'y'.

Reorder the terms:
-10 + 4 + 7y + -1y2 = -4 + y2 + 4 + -1y2

Combine like terms: -10 + 4 = -6
-6 + 7y + -1y2 = -4 + y2 + 4 + -1y2

Reorder the terms:
-6 + 7y + -1y2 = -4 + 4 + y2 + -1y2

Combine like terms: -4 + 4 = 0
-6 + 7y + -1y2 = 0 + y2 + -1y2
-6 + 7y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-6 + 7y + -1y2 = 0

Factor a trinomial.
(-6 + y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {6, 1}