(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.
(-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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