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

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

Simplifying
(x + -3)(-1x + 7) = 0

Reorder the terms:
(-3 + x)(-1x + 7) = 0

Reorder the terms:
(-3 + x)(7 + -1x) = 0

Multiply (-3 + x) * (7 + -1x)
(-3(7 + -1x) + x(7 + -1x)) = 0
((7 * -3 + -1x * -3) + x(7 + -1x)) = 0
((-21 + 3x) + x(7 + -1x)) = 0
(-21 + 3x + (7 * x + -1x * x)) = 0
(-21 + 3x + (7x + -1x2)) = 0

Combine like terms: 3x + 7x = 10x
(-21 + 10x + -1x2) = 0

Solving
-21 + 10x + -1x2 = 0

Solving for variable 'x'.

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}