6(x-2)(2x+9)=0

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Solution for 6(x-2)(2x+9)=0 equation: 


Simplifying
6(x + -2)(2x + 9) = 0

Reorder the terms:
6(-2 + x)(2x + 9) = 0

Reorder the terms:
6(-2 + x)(9 + 2x) = 0

Multiply (-2 + x) * (9 + 2x)
6(-2(9 + 2x) + x(9 + 2x)) = 0
6((9 * -2 + 2x * -2) + x(9 + 2x)) = 0
6((-18 + -4x) + x(9 + 2x)) = 0
6(-18 + -4x + (9 * x + 2x * x)) = 0
6(-18 + -4x + (9x + 2x2)) = 0

Combine like terms: -4x + 9x = 5x
6(-18 + 5x + 2x2) = 0
(-18 * 6 + 5x * 6 + 2x2 * 6) = 0
(-108 + 30x + 12x2) = 0

Solving
-108 + 30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + 5x + 2x2) = 0

Factor a trinomial.
6((-9 + -2x)(2 + -1x)) = 0

Ignore the factor 6.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.5, 2}

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