(x-5)(x+2)=8

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Solution for (x-5)(x+2)=8 equation: 


Simplifying
(x + -5)(x + 2) = 8

Reorder the terms:
(-5 + x)(x + 2) = 8

Reorder the terms:
(-5 + x)(2 + x) = 8

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x)) = 8
((2 * -5 + x * -5) + x(2 + x)) = 8
((-10 + -5x) + x(2 + x)) = 8
(-10 + -5x + (2 * x + x * x)) = 8
(-10 + -5x + (2x + x2)) = 8

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2) = 8

Solving
-10 + -3x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + -3x + x2 = 8 + -8

Combine like terms: -10 + -8 = -18
-18 + -3x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}

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