6(4x-3)(2x+9)=0

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Solution for 6(4x-3)(2x+9)=0 equation: 


Simplifying
6(4x + -3)(2x + 9) = 0

Reorder the terms:
6(-3 + 4x)(2x + 9) = 0

Reorder the terms:
6(-3 + 4x)(9 + 2x) = 0

Multiply (-3 + 4x) * (9 + 2x)
6(-3(9 + 2x) + 4x * (9 + 2x)) = 0
6((9 * -3 + 2x * -3) + 4x * (9 + 2x)) = 0
6((-27 + -6x) + 4x * (9 + 2x)) = 0
6(-27 + -6x + (9 * 4x + 2x * 4x)) = 0
6(-27 + -6x + (36x + 8x2)) = 0

Combine like terms: -6x + 36x = 30x
6(-27 + 30x + 8x2) = 0
(-27 * 6 + 30x * 6 + 8x2 * 6) = 0
(-162 + 180x + 48x2) = 0

Solving
-162 + 180x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-27 + 30x + 8x2) = 0

Factor a trinomial.
6((-9 + -2x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-4.5, 0.75}

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