(x-6)(x-14)=240

Solution for (x-6)(x-14)=240 equation:

Simplifying
(x + -6)(x + -14) = 240

Reorder the terms:
(-6 + x)(x + -14) = 240

Reorder the terms:
(-6 + x)(-14 + x) = 240

Multiply (-6 + x) * (-14 + x)
(-6(-14 + x) + x(-14 + x)) = 240
((-14 * -6 + x * -6) + x(-14 + x)) = 240
((84 + -6x) + x(-14 + x)) = 240
(84 + -6x + (-14 * x + x * x)) = 240
(84 + -6x + (-14x + x2)) = 240

Combine like terms: -6x + -14x = -20x
(84 + -20x + x2) = 240

Solving
84 + -20x + x2 = 240

Solving for variable 'x'.

Reorder the terms:
84 + -240 + -20x + x2 = 240 + -240

Combine like terms: 84 + -240 = -156
-156 + -20x + x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-156 + -20x + x2 = 0

Factor a trinomial.
(-6 + -1x)(26 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(26 + -1x)' equal to zero and attempt to solve:

Simplifying
26 + -1x = 0

Solving
26 + -1x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x = 0 + -26
-1x = 0 + -26

Combine like terms: 0 + -26 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26
Solution
x = {-6, 26}