(X-2)(X+5)-8=0

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Solution for (X-2)(X+5)-8=0 equation: 


Simplifying
(X + -2)(X + 5) + -8 = 0

Reorder the terms:
(-2 + X)(X + 5) + -8 = 0

Reorder the terms:
(-2 + X)(5 + X) + -8 = 0

Multiply (-2 + X) * (5 + X)
(-2(5 + X) + X(5 + X)) + -8 = 0
((5 * -2 + X * -2) + X(5 + X)) + -8 = 0
((-10 + -2X) + X(5 + X)) + -8 = 0
(-10 + -2X + (5 * X + X * X)) + -8 = 0
(-10 + -2X + (5X + X2)) + -8 = 0

Combine like terms: -2X + 5X = 3X
(-10 + 3X + X2) + -8 = 0

Reorder the terms:
-10 + -8 + 3X + X2 = 0

Combine like terms: -10 + -8 = -18
-18 + 3X + X2 = 0

Solving
-18 + 3X + X2 = 0

Solving for variable 'X'.

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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