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

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


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

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

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

Multiply (-2 + x) * (9 + 5x)
12(-2(9 + 5x) + x(9 + 5x)) = 0
12((9 * -2 + 5x * -2) + x(9 + 5x)) = 0
12((-18 + -10x) + x(9 + 5x)) = 0
12(-18 + -10x + (9 * x + 5x * x)) = 0
12(-18 + -10x + (9x + 5x2)) = 0

Combine like terms: -10x + 9x = -1x
12(-18 + -1x + 5x2) = 0
(-18 * 12 + -1x * 12 + 5x2 * 12) = 0
(-216 + -12x + 60x2) = 0

Solving
-216 + -12x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-18 + -1x + 5x2) = 0

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

Ignore the factor 12.

Subproblem 1
Set the factor '(-9 + -5x)' equal to zero and attempt to solve:

Simplifying
-9 + -5x = 0

Solving
-9 + -5x = 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 + -5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x = 0 + 9
-5x = 0 + 9

Combine like terms: 0 + 9 = 9
-5x = 9

Divide each side by '-5'.
x = -1.8

Simplifying
x = -1.8

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 = {-1.8, 2}

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