45=(x-2)(x-14)

Solution for 45=(x-2)(x-14) equation:

Simplifying
45 = (x + -2)(x + -14)

Reorder the terms:
45 = (-2 + x)(x + -14)

Reorder the terms:
45 = (-2 + x)(-14 + x)

Multiply (-2 + x) * (-14 + x)
45 = (-2(-14 + x) + x(-14 + x))
45 = ((-14 * -2 + x * -2) + x(-14 + x))
45 = ((28 + -2x) + x(-14 + x))
45 = (28 + -2x + (-14 * x + x * x))
45 = (28 + -2x + (-14x + x2))

Combine like terms: -2x + -14x = -16x
45 = (28 + -16x + x2)

Solving
45 = 28 + -16x + x2

Solving for variable 'x'.

Combine like terms: 45 + -28 = 17
17 + 16x + -1x2 = 28 + -16x + x2 + -28 + 16x + -1x2

Reorder the terms:
17 + 16x + -1x2 = 28 + -28 + -16x + 16x + x2 + -1x2

Combine like terms: 28 + -28 = 0
17 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2
17 + 16x + -1x2 = -16x + 16x + x2 + -1x2

Combine like terms: -16x + 16x = 0
17 + 16x + -1x2 = 0 + x2 + -1x2
17 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
17 + 16x + -1x2 = 0

Factor a trinomial.
(17 + -1x)(1 + x) = 0

Subproblem 1
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {17, -1}