(x+2)(x+7)=84

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Solution for (x+2)(x+7)=84 equation: 


Simplifying
(x + 2)(x + 7) = 84

Reorder the terms:
(2 + x)(x + 7) = 84

Reorder the terms:
(2 + x)(7 + x) = 84

Multiply (2 + x) * (7 + x)
(2(7 + x) + x(7 + x)) = 84
((7 * 2 + x * 2) + x(7 + x)) = 84
((14 + 2x) + x(7 + x)) = 84
(14 + 2x + (7 * x + x * x)) = 84
(14 + 2x + (7x + x2)) = 84

Combine like terms: 2x + 7x = 9x
(14 + 9x + x2) = 84

Solving
14 + 9x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
14 + -84 + 9x + x2 = 84 + -84

Combine like terms: 14 + -84 = -70
-70 + 9x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-70 + 9x + x2 = 0

Factor a trinomial.
(-14 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-14, 5}

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