(x-13)(x+7)=-84

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Solution for (x-13)(x+7)=-84 equation: 


Simplifying
(x + -13)(x + 7) = -84

Reorder the terms:
(-13 + x)(x + 7) = -84

Reorder the terms:
(-13 + x)(7 + x) = -84

Multiply (-13 + x) * (7 + x)
(-13(7 + x) + x(7 + x)) = -84
((7 * -13 + x * -13) + x(7 + x)) = -84
((-91 + -13x) + x(7 + x)) = -84
(-91 + -13x + (7 * x + x * x)) = -84
(-91 + -13x + (7x + x2)) = -84

Combine like terms: -13x + 7x = -6x
(-91 + -6x + x2) = -84

Solving
-91 + -6x + x2 = -84

Solving for variable 'x'.

Reorder the terms:
-91 + 84 + -6x + x2 = -84 + 84

Combine like terms: -91 + 84 = -7
-7 + -6x + x2 = -84 + 84

Combine like terms: -84 + 84 = 0
-7 + -6x + x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 7}

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