(2x-5)(3x+27)=0

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Solution for (2x-5)(3x+27)=0 equation: 


Simplifying
(2x + -5)(3x + 27) = 0

Reorder the terms:
(-5 + 2x)(3x + 27) = 0

Reorder the terms:
(-5 + 2x)(27 + 3x) = 0

Multiply (-5 + 2x) * (27 + 3x)
(-5(27 + 3x) + 2x * (27 + 3x)) = 0
((27 * -5 + 3x * -5) + 2x * (27 + 3x)) = 0
((-135 + -15x) + 2x * (27 + 3x)) = 0
(-135 + -15x + (27 * 2x + 3x * 2x)) = 0
(-135 + -15x + (54x + 6x2)) = 0

Combine like terms: -15x + 54x = 39x
(-135 + 39x + 6x2) = 0

Solving
-135 + 39x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + 13x + 2x2) = 0

Factor a trinomial.
3((-9 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-9, 2.5}

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