y^2+7y-18=3y-6

Solution for y^2+7y-18=3y-6 equation:

Simplifying
y2 + 7y + -18 = 3y + -6

Reorder the terms:
-18 + 7y + y2 = 3y + -6

Reorder the terms:
-18 + 7y + y2 = -6 + 3y

Solving
-18 + 7y + y2 = -6 + 3y

Solving for variable 'y'.

Reorder the terms:
-18 + 6 + 7y + -3y + y2 = -6 + 3y + 6 + -3y

Combine like terms: -18 + 6 = -12
-12 + 7y + -3y + y2 = -6 + 3y + 6 + -3y

Combine like terms: 7y + -3y = 4y
-12 + 4y + y2 = -6 + 3y + 6 + -3y

Reorder the terms:
-12 + 4y + y2 = -6 + 6 + 3y + -3y

Combine like terms: -6 + 6 = 0
-12 + 4y + y2 = 0 + 3y + -3y
-12 + 4y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-12 + 4y + y2 = 0

Factor a trinomial.
(-6 + -1y)(2 + -1y) = 0

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

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 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 + -1y = 0 + 6

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

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

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
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
Solution
y = {-6, 2}