66=(x+7)(x+12)-(12)(7)

Solution for 66=(x+7)(x+12)-(12)(7) equation:

Simplifying
66 = (x + 7)(x + 12) + -1(12)(7)

Reorder the terms:
66 = (7 + x)(x + 12) + -1(12)(7)

Reorder the terms:
66 = (7 + x)(12 + x) + -1(12)(7)

Multiply (7 + x) * (12 + x)
66 = (7(12 + x) + x(12 + x)) + -1(12)(7)
66 = ((12 * 7 + x * 7) + x(12 + x)) + -1(12)(7)
66 = ((84 + 7x) + x(12 + x)) + -1(12)(7)
66 = (84 + 7x + (12 * x + x * x)) + -1(12)(7)
66 = (84 + 7x + (12x + x2)) + -1(12)(7)

Combine like terms: 7x + 12x = 19x
66 = (84 + 19x + x2) + -1(12)(7)

Multiply -1 * 12
66 = 84 + 19x + x2 + -12 * 7

Multiply -12 * 7
66 = 84 + 19x + x2 + -84

Reorder the terms:
66 = 84 + -84 + 19x + x2

Combine like terms: 84 + -84 = 0
66 = 0 + 19x + x2
66 = 19x + x2

Solving
66 = 19x + x2

Solving for variable 'x'.

Reorder the terms:
66 + -19x + -1x2 = 19x + -19x + x2 + -1x2

Combine like terms: 19x + -19x = 0
66 + -19x + -1x2 = 0 + x2 + -1x2
66 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
66 + -19x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(22 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(22 + x)' equal to zero and attempt to solve:

Simplifying
22 + x = 0

Solving
22 + x = 0

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

Add '-22' to each side of the equation.
22 + -22 + x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + x = 0 + -22
x = 0 + -22

Combine like terms: 0 + -22 = -22
x = -22

Simplifying
x = -22
Solution
x = {3, -22}