(x+2)(x-7)=-18

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Solution for (x+2)(x-7)=-18 equation: 


Simplifying
(x + 2)(x + -7) = -18

Reorder the terms:
(2 + x)(x + -7) = -18

Reorder the terms:
(2 + x)(-7 + x) = -18

Multiply (2 + x) * (-7 + x)
(2(-7 + x) + x(-7 + x)) = -18
((-7 * 2 + x * 2) + x(-7 + x)) = -18
((-14 + 2x) + x(-7 + x)) = -18
(-14 + 2x + (-7 * x + x * x)) = -18
(-14 + 2x + (-7x + x2)) = -18

Combine like terms: 2x + -7x = -5x
(-14 + -5x + x2) = -18

Solving
-14 + -5x + x2 = -18

Solving for variable 'x'.

Reorder the terms:
-14 + 18 + -5x + x2 = -18 + 18

Combine like terms: -14 + 18 = 4
4 + -5x + x2 = -18 + 18

Combine like terms: -18 + 18 = 0
4 + -5x + x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

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

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

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

Simplifying
x = 4
Solution
x = {1, 4}

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