(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.
(-6 + -1x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-6, 3}

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