0=(x-3)(x-7)

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

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

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

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

Multiply (-3 + x) * (-7 + x)
0 = (-3(-7 + x) + x(-7 + x))
0 = ((-7 * -3 + x * -3) + x(-7 + x))
0 = ((21 + -3x) + x(-7 + x))
0 = (21 + -3x + (-7 * x + x * x))
0 = (21 + -3x + (-7x + x2))

Combine like terms: -3x + -7x = -10x
0 = (21 + -10x + x2)

Solving
0 = 21 + -10x + x2

Solving for variable 'x'.

Combine like terms: 0 + -21 = -21
-21 + 10x + -1x2 = 21 + -10x + x2 + -21 + 10x + -1x2

Reorder the terms:
-21 + 10x + -1x2 = 21 + -21 + -10x + 10x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-21 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-21 + 10x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-21 + 10x + -1x2 = 0 + x2 + -1x2
-21 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 10x + -1x2 = 0

Factor a trinomial.
(-7 + x)(3 + -1x) = 0

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

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Subproblem 2
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
Solution
x = {7, 3}