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

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

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

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

Reorder the terms for easier multiplication:
x(-3 + x) + 7(x + -3) = 0
(-3 * x + x * x) + 7(x + -3) = 0
(-3x + x2) + 7(x + -3) = 0

Reorder the terms:
-3x + x2 + 7(-3 + x) = 0
-3x + x2 + (-3 * 7 + x * 7) = 0
-3x + x2 + (-21 + 7x) = 0

Reorder the terms:
-21 + -3x + 7x + x2 = 0

Combine like terms: -3x + 7x = 4x
-21 + 4x + x2 = 0

Solving
-21 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(3 + -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 '(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}