(x-3)(x-7)=21

Solution for (x-3)(x-7)=21 equation:

Simplifying
(x + -3)(x + -7) = 21

Reorder the terms:
(-3 + x)(x + -7) = 21

Reorder the terms:
(-3 + x)(-7 + x) = 21

Multiply (-3 + x) * (-7 + x)
(-3(-7 + x) + x(-7 + x)) = 21
((-7 * -3 + x * -3) + x(-7 + x)) = 21
((21 + -3x) + x(-7 + x)) = 21
(21 + -3x + (-7 * x + x * x)) = 21
(21 + -3x + (-7x + x2)) = 21

Combine like terms: -3x + -7x = -10x
(21 + -10x + x2) = 21

Add '-21' to each side of the equation.
21 + -10x + -21 + x2 = 21 + -21

Reorder the terms:
21 + -21 + -10x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
0 + -10x + x2 = 21 + -21
-10x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-10x + x2 = 0

Solving
-10x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 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 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, 10}