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

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


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

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

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

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

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

Solving
-10 + -3x + x2 = 18

Solving for variable 'x'.

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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 7}

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