(x-2)(x+5)-18=0

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Solution for (x-2)(x+5)-18=0 equation:


Simplifying
(x + -2)(x + 5) + -18 = 0

Reorder the terms:
(-2 + x)(x + 5) + -18 = 0

Reorder the terms:
(-2 + x)(5 + x) + -18 = 0

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) + -18 = 0
((5 * -2 + x * -2) + x(5 + x)) + -18 = 0
((-10 + -2x) + x(5 + x)) + -18 = 0
(-10 + -2x + (5 * x + x * x)) + -18 = 0
(-10 + -2x + (5x + x2)) + -18 = 0

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) + -18 = 0

Reorder the terms:
-10 + -18 + 3x + x2 = 0

Combine like terms: -10 + -18 = -28
-28 + 3x + x2 = 0

Solving
-28 + 3x + x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

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

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

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

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

Simplifying
x = -7

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 = {-7, 4}

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