(x+3)(x-5)=84

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Solution for (x+3)(x-5)=84 equation: 


Simplifying
(x + 3)(x + -5) = 84

Reorder the terms:
(3 + x)(x + -5) = 84

Reorder the terms:
(3 + x)(-5 + x) = 84

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) = 84
((-5 * 3 + x * 3) + x(-5 + x)) = 84
((-15 + 3x) + x(-5 + x)) = 84
(-15 + 3x + (-5 * x + x * x)) = 84
(-15 + 3x + (-5x + x2)) = 84

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) = 84

Solving
-15 + -2x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
-15 + -84 + -2x + x2 = 84 + -84

Combine like terms: -15 + -84 = -99
-99 + -2x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-99 + -2x + x2 = 0

Factor a trinomial.
(-9 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-9, 11}

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