(3x-27)(x+8)=0

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Solution for (3x-27)(x+8)=0 equation: 


Simplifying
(3x + -27)(x + 8) = 0

Reorder the terms:
(-27 + 3x)(x + 8) = 0

Reorder the terms:
(-27 + 3x)(8 + x) = 0

Multiply (-27 + 3x) * (8 + x)
(-27(8 + x) + 3x * (8 + x)) = 0
((8 * -27 + x * -27) + 3x * (8 + x)) = 0
((-216 + -27x) + 3x * (8 + x)) = 0
(-216 + -27x + (8 * 3x + x * 3x)) = 0
(-216 + -27x + (24x + 3x2)) = 0

Combine like terms: -27x + 24x = -3x
(-216 + -3x + 3x2) = 0

Solving
-216 + -3x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-72 + -1x + x2) = 0

Factor a trinomial.
3((-8 + -1x)(9 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-8, 9}

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