((3x)(3x))-15x+1=3(x+2)(-5+x)

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Solution for ((3x)(3x))-15x+1=3(x+2)(-5+x) equation: 


Simplifying
((3x)(3x)) + -15x + 1 = 3(x + 2)(-5 + x)

Remove parenthesis around (3x)
(3x(3x)) + -15x + 1 = 3(x + 2)(-5 + x)

Remove parenthesis around (3x)
(3x * 3x) + -15x + 1 = 3(x + 2)(-5 + x)

Reorder the terms for easier multiplication:
(3 * 3x * x) + -15x + 1 = 3(x + 2)(-5 + x)

Multiply 3 * 3
(9x * x) + -15x + 1 = 3(x + 2)(-5 + x)

Multiply x * x
(9x2) + -15x + 1 = 3(x + 2)(-5 + x)

Reorder the terms:
1 + -15x + (9x2) = 3(x + 2)(-5 + x)

Reorder the terms:
1 + -15x + (9x2) = 3(2 + x)(-5 + x)

Multiply (2 + x) * (-5 + x)
1 + -15x + (9x2) = 3(2(-5 + x) + x(-5 + x))
1 + -15x + (9x2) = 3((-5 * 2 + x * 2) + x(-5 + x))
1 + -15x + (9x2) = 3((-10 + 2x) + x(-5 + x))
1 + -15x + (9x2) = 3(-10 + 2x + (-5 * x + x * x))
1 + -15x + (9x2) = 3(-10 + 2x + (-5x + x2))

Combine like terms: 2x + -5x = -3x
1 + -15x + (9x2) = 3(-10 + -3x + x2)
1 + -15x + (9x2) = (-10 * 3 + -3x * 3 + x2 * 3)
1 + -15x + (9x2) = (-30 + -9x + 3x2)

Solving
1 + -15x + (9x2) = -30 + -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
1 + 30 + -15x + 9x + (9x2) + -3x2 = -30 + -9x + 3x2 + 30 + 9x + -3x2

Combine like terms: 1 + 30 = 31
31 + -15x + 9x + (9x2) + -3x2 = -30 + -9x + 3x2 + 30 + 9x + -3x2

Combine like terms: -15x + 9x = -6x
31 + -6x + (9x2) + -3x2 = -30 + -9x + 3x2 + 30 + 9x + -3x2

Combine like terms: (9x2) + -3x2 = 6x2
31 + -6x + 6x2 = -30 + -9x + 3x2 + 30 + 9x + -3x2

Reorder the terms:
31 + -6x + 6x2 = -30 + 30 + -9x + 9x + 3x2 + -3x2

Combine like terms: -30 + 30 = 0
31 + -6x + 6x2 = 0 + -9x + 9x + 3x2 + -3x2
31 + -6x + 6x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
31 + -6x + 6x2 = 0 + 3x2 + -3x2
31 + -6x + 6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
31 + -6x + 6x2 = 0

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

Divide each side by '6'.
5.166666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-5.166666667' to each side of the equation.
5.166666667 + -1x + -5.166666667 + x2 = 0 + -5.166666667

Reorder the terms:
5.166666667 + -5.166666667 + -1x + x2 = 0 + -5.166666667

Combine like terms: 5.166666667 + -5.166666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + -5.166666667
-1x + x2 = 0 + -5.166666667

Combine like terms: 0 + -5.166666667 = -5.166666667
-1x + x2 = -5.166666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -5.166666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -5.166666667 + 0.25

Combine like terms: -5.166666667 + 0.25 = -4.916666667
0.25 + -1x + x2 = -4.916666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -4.916666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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