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

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

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

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

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

Multiply (-5 + 3x) * (21 + x)
x = (-5(21 + x) + 3x * (21 + x))
x = ((21 * -5 + x * -5) + 3x * (21 + x))
x = ((-105 + -5x) + 3x * (21 + x))
x = (-105 + -5x + (21 * 3x + x * 3x))
x = (-105 + -5x + (63x + 3x2))

Combine like terms: -5x + 63x = 58x
x = (-105 + 58x + 3x2)

Solving
x = -105 + 58x + 3x2

Solving for variable 'x'.

Reorder the terms:
105 + x + -58x + -3x2 = -105 + 58x + 3x2 + 105 + -58x + -3x2

Combine like terms: x + -58x = -57x
105 + -57x + -3x2 = -105 + 58x + 3x2 + 105 + -58x + -3x2

Reorder the terms:
105 + -57x + -3x2 = -105 + 105 + 58x + -58x + 3x2 + -3x2

Combine like terms: -105 + 105 = 0
105 + -57x + -3x2 = 0 + 58x + -58x + 3x2 + -3x2
105 + -57x + -3x2 = 58x + -58x + 3x2 + -3x2

Combine like terms: 58x + -58x = 0
105 + -57x + -3x2 = 0 + 3x2 + -3x2
105 + -57x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
105 + -57x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + -19x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(35 + -19x + -1x2)' equal to zero and attempt to solve:

Simplifying
35 + -19x + -1x2 = 0

Solving
35 + -19x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-35 + 19x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 19x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 19x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 19x + x2 = 0 + 35
19x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
19x + x2 = 35

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 35 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 35 + 90.25

Combine like terms: 35 + 90.25 = 125.25
90.25 + 19x + x2 = 125.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 125.25

Calculate the square root of the right side: 11.191514643

Break this problem into two subproblems by setting 
(x + 9.5) equal to 11.191514643 and -11.191514643.

Subproblem 1
x + 9.5 = 11.191514643

Simplifying
x + 9.5 = 11.191514643

Reorder the terms:
9.5 + x = 11.191514643

Solving
9.5 + x = 11.191514643

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 11.191514643 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 11.191514643 + -9.5
x = 11.191514643 + -9.5

Combine like terms: 11.191514643 + -9.5 = 1.691514643
x = 1.691514643

Simplifying
x = 1.691514643

Subproblem 2
x + 9.5 = -11.191514643

Simplifying
x + 9.5 = -11.191514643

Reorder the terms:
9.5 + x = -11.191514643

Solving
9.5 + x = -11.191514643

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -11.191514643 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -11.191514643 + -9.5
x = -11.191514643 + -9.5

Combine like terms: -11.191514643 + -9.5 = -20.691514643
x = -20.691514643

Simplifying
x = -20.691514643

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.691514643, -20.691514643}
Solution
x = {1.691514643, -20.691514643}