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

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


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

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

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

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

Combine like terms: 7x + 2x = 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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