3(x+5)*3x=21

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


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

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

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

Multiply 3 * 3
9x(5 + x) = 21
(5 * 9x + x * 9x) = 21
(45x + 9x2) = 21

Solving
45x + 9x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 45x + 9x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 45x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 15x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-7 + 15x + 3x2 = 0

Solving
-7 + 15x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 5x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 5x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + 2.333333333
5x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
5x + x2 = 2.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.333333333 + 6.25

Combine like terms: 2.333333333 + 6.25 = 8.583333333
6.25 + 5x + x2 = 8.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.583333333

Calculate the square root of the right side: 2.929732638

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.929732638 and -2.929732638.


Subproblem 1
x + 2.5 = 2.929732638

Simplifying
x + 2.5 = 2.929732638

Reorder the terms:
2.5 + x = 2.929732638

Solving
2.5 + x = 2.929732638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.929732638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.929732638 + -2.5
x = 2.929732638 + -2.5

Combine like terms: 2.929732638 + -2.5 = 0.429732638
x = 0.429732638

Simplifying
x = 0.429732638


Subproblem 2
x + 2.5 = -2.929732638

Simplifying
x + 2.5 = -2.929732638

Reorder the terms:
2.5 + x = -2.929732638

Solving
2.5 + x = -2.929732638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.929732638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.929732638 + -2.5
x = -2.929732638 + -2.5

Combine like terms: -2.929732638 + -2.5 = -5.429732638
x = -5.429732638

Simplifying
x = -5.429732638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.429732638, -5.429732638}
Solution
x = {0.429732638, -5.429732638}

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