(y-2)(y+5)=18

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Solution for (y-2)(y+5)=18 equation: 


Simplifying
(y + -2)(y + 5) = 18

Reorder the terms:
(-2 + y)(y + 5) = 18

Reorder the terms:
(-2 + y)(5 + y) = 18

Multiply (-2 + y) * (5 + y)
(-2(5 + y) + y(5 + y)) = 18
((5 * -2 + y * -2) + y(5 + y)) = 18
((-10 + -2y) + y(5 + y)) = 18
(-10 + -2y + (5 * y + y * y)) = 18
(-10 + -2y + (5y + y2)) = 18

Combine like terms: -2y + 5y = 3y
(-10 + 3y + y2) = 18

Solving
-10 + 3y + y2 = 18

Solving for variable 'y'.

Reorder the terms:
-10 + -18 + 3y + y2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + 3y + y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + 3y + y2 = 0

Factor a trinomial.
(-7 + -1y)(4 + -1y) = 0


Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

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

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

Divide each side by '-1'.
y = -7

Simplifying
y = -7

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-7, 4}

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