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

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


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

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

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

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

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

Solving
84 = 14 + 9x + x2

Solving for variable 'x'.

Combine like terms: 84 + -14 = 70
70 + -9x + -1x2 = 14 + 9x + x2 + -14 + -9x + -1x2

Reorder the terms:
70 + -9x + -1x2 = 14 + -14 + 9x + -9x + x2 + -1x2

Combine like terms: 14 + -14 = 0
70 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2
70 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
70 + -9x + -1x2 = 0 + x2 + -1x2
70 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
70 + -9x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 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 + x = 0 + -14

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

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

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

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