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

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Solution for 6(x-3)+5=-3x(-5+x) equation: 


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

Reorder the terms:
6(-3 + x) + 5 = -3x(-5 + x)
(-3 * 6 + x * 6) + 5 = -3x(-5 + x)
(-18 + 6x) + 5 = -3x(-5 + x)

Reorder the terms:
-18 + 5 + 6x = -3x(-5 + x)

Combine like terms: -18 + 5 = -13
-13 + 6x = -3x(-5 + x)
-13 + 6x = (-5 * -3x + x * -3x)
-13 + 6x = (15x + -3x2)

Solving
-13 + 6x = 15x + -3x2

Solving for variable 'x'.

Combine like terms: 6x + -15x = -9x
-13 + -9x + 3x2 = 15x + -3x2 + -15x + 3x2

Reorder the terms:
-13 + -9x + 3x2 = 15x + -15x + -3x2 + 3x2

Combine like terms: 15x + -15x = 0
-13 + -9x + 3x2 = 0 + -3x2 + 3x2
-13 + -9x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-13 + -9x + 3x2 = 0

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

Divide each side by '3'.
-4.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + -3x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + -3x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 4.333333333
-3x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
-3x + x2 = 4.333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 4.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 4.333333333 + 2.25

Combine like terms: 4.333333333 + 2.25 = 6.583333333
2.25 + -3x + x2 = 6.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 6.583333333

Calculate the square root of the right side: 2.56580072

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.56580072 and -2.56580072.


Subproblem 1
x + -1.5 = 2.56580072

Simplifying
x + -1.5 = 2.56580072

Reorder the terms:
-1.5 + x = 2.56580072

Solving
-1.5 + x = 2.56580072

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.56580072 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.56580072 + 1.5
x = 2.56580072 + 1.5

Combine like terms: 2.56580072 + 1.5 = 4.06580072
x = 4.06580072

Simplifying
x = 4.06580072


Subproblem 2
x + -1.5 = -2.56580072

Simplifying
x + -1.5 = -2.56580072

Reorder the terms:
-1.5 + x = -2.56580072

Solving
-1.5 + x = -2.56580072

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.56580072 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.56580072 + 1.5
x = -2.56580072 + 1.5

Combine like terms: -2.56580072 + 1.5 = -1.06580072
x = -1.06580072

Simplifying
x = -1.06580072


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.06580072, -1.06580072}

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