6x-9=3x(3x)

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Solution for 6x-9=3x(3x) equation: 


Simplifying
6x + -9 = 3x(3x)

Reorder the terms:
-9 + 6x = 3x(3x)

Remove parenthesis around (3x)
-9 + 6x = 3x * 3x

Reorder the terms for easier multiplication:
-9 + 6x = 3 * 3x * x

Multiply 3 * 3
-9 + 6x = 9x * x

Multiply x * x
-9 + 6x = 9x2

Solving
-9 + 6x = 9x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2x + -3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + 2x + -3x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x + -3x2 = 0

Solving
-3 + 2x + -3x2 = 0

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

Divide each side by '-3'.
1 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.6666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -0.6666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.6666666667x + x2 = 0 + -1
-0.6666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.6666666667x + x2 = -1

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -1 + 0.1111111112

Combine like terms: -1 + 0.1111111112 = -0.8888888888
0.1111111112 + -0.6666666667x + x2 = -0.8888888888

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -0.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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