(x+2)(x+7)=66

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Solution for (x+2)(x+7)=66 equation: 


Simplifying
(x + 2)(x + 7) = 66

Reorder the terms:
(2 + x)(x + 7) = 66

Reorder the terms:
(2 + x)(7 + x) = 66

Multiply (2 + x) * (7 + x)
(2(7 + x) + x(7 + x)) = 66
((7 * 2 + x * 2) + x(7 + x)) = 66
((14 + 2x) + x(7 + x)) = 66
(14 + 2x + (7 * x + x * x)) = 66
(14 + 2x + (7x + x2)) = 66

Combine like terms: 2x + 7x = 9x
(14 + 9x + x2) = 66

Solving
14 + 9x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
14 + -66 + 9x + x2 = 66 + -66

Combine like terms: 14 + -66 = -52
-52 + 9x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-52 + 9x + x2 = 0

Factor a trinomial.
(-13 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-13, 4}

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