12(x-5)(2x+9)=0

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Solution for 12(x-5)(2x+9)=0 equation: 


Simplifying
12(x + -5)(2x + 9) = 0

Reorder the terms:
12(-5 + x)(2x + 9) = 0

Reorder the terms:
12(-5 + x)(9 + 2x) = 0

Multiply (-5 + x) * (9 + 2x)
12(-5(9 + 2x) + x(9 + 2x)) = 0
12((9 * -5 + 2x * -5) + x(9 + 2x)) = 0
12((-45 + -10x) + x(9 + 2x)) = 0
12(-45 + -10x + (9 * x + 2x * x)) = 0
12(-45 + -10x + (9x + 2x2)) = 0

Combine like terms: -10x + 9x = -1x
12(-45 + -1x + 2x2) = 0
(-45 * 12 + -1x * 12 + 2x2 * 12) = 0
(-540 + -12x + 24x2) = 0

Solving
-540 + -12x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-45 + -1x + 2x2) = 0

Factor a trinomial.
12((-9 + -2x)(5 + -1x)) = 0

Ignore the factor 12.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4.5, 5}

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