-3(-x+7)5x=-21

Solution for -3(-x+7)5x=-21 equation:

Simplifying
-3(-1x + 7) * 5x = -21

Reorder the terms:
-3(7 + -1x) * 5x = -21

Reorder the terms for easier multiplication:
-3 * 5x(7 + -1x) = -21

Multiply -3 * 5
-15x(7 + -1x) = -21
(7 * -15x + -1x * -15x) = -21
(-105x + 15x2) = -21

Solving
-105x + 15x2 = -21

Solving for variable 'x'.

Reorder the terms:
21 + -105x + 15x2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + -105x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -35x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + -35x + 5x2)' equal to zero and attempt to solve:

Simplifying
7 + -35x + 5x2 = 0

Solving
7 + -35x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.4 + -7x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -7x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -7x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -7x + x2 = 0 + -1.4
-7x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-7x + x2 = -1.4

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -1.4 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -1.4 + 12.25

Combine like terms: -1.4 + 12.25 = 10.85
12.25 + -7x + x2 = 10.85

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 10.85

Calculate the square root of the right side: 3.293933818

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.293933818 and -3.293933818.

Subproblem 1
x + -3.5 = 3.293933818

Simplifying
x + -3.5 = 3.293933818

Reorder the terms:
-3.5 + x = 3.293933818

Solving
-3.5 + x = 3.293933818

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.293933818 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.293933818 + 3.5
x = 3.293933818 + 3.5

Combine like terms: 3.293933818 + 3.5 = 6.793933818
x = 6.793933818

Simplifying
x = 6.793933818

Subproblem 2
x + -3.5 = -3.293933818

Simplifying
x + -3.5 = -3.293933818

Reorder the terms:
-3.5 + x = -3.293933818

Solving
-3.5 + x = -3.293933818

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.293933818 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.293933818 + 3.5
x = -3.293933818 + 3.5

Combine like terms: -3.293933818 + 3.5 = 0.206066182
x = 0.206066182

Simplifying
x = 0.206066182

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.793933818, 0.206066182}
Solution
x = {6.793933818, 0.206066182}