(X-1)(X-2)=72

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Solution for (X-1)(X-2)=72 equation: 


Simplifying
(X + -1)(X + -2) = 72

Reorder the terms:
(-1 + X)(X + -2) = 72

Reorder the terms:
(-1 + X)(-2 + X) = 72

Multiply (-1 + X) * (-2 + X)
(-1(-2 + X) + X(-2 + X)) = 72
((-2 * -1 + X * -1) + X(-2 + X)) = 72
((2 + -1X) + X(-2 + X)) = 72
(2 + -1X + (-2 * X + X * X)) = 72
(2 + -1X + (-2X + X2)) = 72

Combine like terms: -1X + -2X = -3X
(2 + -3X + X2) = 72

Solving
2 + -3X + X2 = 72

Solving for variable 'X'.

Reorder the terms:
2 + -72 + -3X + X2 = 72 + -72

Combine like terms: 2 + -72 = -70
-70 + -3X + X2 = 72 + -72

Combine like terms: 72 + -72 = 0
-70 + -3X + X2 = 0

Factor a trinomial.
(-7 + -1X)(10 + -1X) = 0


Subproblem 1
Set the factor '(-7 + -1X)' equal to zero and attempt to solve:

Simplifying
-7 + -1X = 0

Solving
-7 + -1X = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1X = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1X = 0 + 7
-1X = 0 + 7

Combine like terms: 0 + 7 = 7
-1X = 7

Divide each side by '-1'.
X = -7

Simplifying
X = -7

Subproblem 2
Set the factor '(10 + -1X)' equal to zero and attempt to solve:

Simplifying
10 + -1X = 0

Solving
10 + -1X = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1X = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1X = 0 + -10
-1X = 0 + -10

Combine like terms: 0 + -10 = -10
-1X = -10

Divide each side by '-1'.
X = 10

Simplifying
X = 10
Solution
X = {-7, 10}

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