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

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

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

Reorder the terms:
21x + -7x2 + -1(-3 + x) = 0
21x + -7x2 + (-3 * -1 + x * -1) = 0
21x + -7x2 + (3 + -1x) = 0

Reorder the terms:
3 + 21x + -1x + -7x2 = 0

Combine like terms: 21x + -1x = 20x
3 + 20x + -7x2 = 0

Solving
3 + 20x + -7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(1 + 7x) = 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 '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {3, -0.1428571429}