(x-2)(x+7)=-8

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Solution for (x-2)(x+7)=-8 equation: 


Simplifying
(x + -2)(x + 7) = -8

Reorder the terms:
(-2 + x)(x + 7) = -8

Reorder the terms:
(-2 + x)(7 + x) = -8

Multiply (-2 + x) * (7 + x)
(-2(7 + x) + x(7 + x)) = -8
((7 * -2 + x * -2) + x(7 + x)) = -8
((-14 + -2x) + x(7 + x)) = -8
(-14 + -2x + (7 * x + x * x)) = -8
(-14 + -2x + (7x + x2)) = -8

Combine like terms: -2x + 7x = 5x
(-14 + 5x + x2) = -8

Solving
-14 + 5x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-14 + 8 + 5x + x2 = -8 + 8

Combine like terms: -14 + 8 = -6
-6 + 5x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}

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