9(x-3)=-3x(2x+4)

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Solution for 9(x-3)=-3x(2x+4) equation: 


Simplifying
9(x + -3) = -3x(2x + 4)

Reorder the terms:
9(-3 + x) = -3x(2x + 4)
(-3 * 9 + x * 9) = -3x(2x + 4)
(-27 + 9x) = -3x(2x + 4)

Reorder the terms:
-27 + 9x = -3x(4 + 2x)
-27 + 9x = (4 * -3x + 2x * -3x)
-27 + 9x = (-12x + -6x2)

Solving
-27 + 9x = -12x + -6x2

Solving for variable 'x'.

Combine like terms: 9x + 12x = 21x
-27 + 21x + 6x2 = -12x + -6x2 + 12x + 6x2

Reorder the terms:
-27 + 21x + 6x2 = -12x + 12x + -6x2 + 6x2

Combine like terms: -12x + 12x = 0
-27 + 21x + 6x2 = 0 + -6x2 + 6x2
-27 + 21x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-27 + 21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 7x + 2x2) = 0

Factor a trinomial.
3((-9 + -2x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-4.5, 1}

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