(X-7)(X-3)=0

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Solution for (X-7)(X-3)=0 equation: 


Simplifying
(X + -7)(X + -3) = 0

Reorder the terms:
(-7 + X)(X + -3) = 0

Reorder the terms:
(-7 + X)(-3 + X) = 0

Multiply (-7 + X) * (-3 + X)
(-7(-3 + X) + X(-3 + X)) = 0
((-3 * -7 + X * -7) + X(-3 + X)) = 0
((21 + -7X) + X(-3 + X)) = 0
(21 + -7X + (-3 * X + X * X)) = 0
(21 + -7X + (-3X + X2)) = 0

Combine like terms: -7X + -3X = -10X
(21 + -10X + X2) = 0

Solving
21 + -10X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(3 + -1X)(7 + -1X) = 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 '(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
Solution
X = {3, 7}

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