3x+9=6x(x-2)

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Solution for 3x+9=6x(x-2) equation: 


Simplifying
3x + 9 = 6x(x + -2)

Reorder the terms:
9 + 3x = 6x(x + -2)

Reorder the terms:
9 + 3x = 6x(-2 + x)
9 + 3x = (-2 * 6x + x * 6x)
9 + 3x = (-12x + 6x2)

Solving
9 + 3x = -12x + 6x2

Solving for variable 'x'.

Combine like terms: 3x + 12x = 15x
9 + 15x + -6x2 = -12x + 6x2 + 12x + -6x2

Reorder the terms:
9 + 15x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
9 + 15x + -6x2 = 0 + 6x2 + -6x2
9 + 15x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
9 + 15x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 5x + -2x2) = 0

Factor a trinomial.
3((3 + -1x)(1 + 2x)) = 0

Ignore the factor 3.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {3, -0.5}

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