2x(2x-9)(6x+5)=0

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Solution for 2x(2x-9)(6x+5)=0 equation: 


Simplifying
2x(2x + -9)(6x + 5) = 0

Reorder the terms:
2x(-9 + 2x)(6x + 5) = 0

Reorder the terms:
2x(-9 + 2x)(5 + 6x) = 0

Multiply (-9 + 2x) * (5 + 6x)
2x(-9(5 + 6x) + 2x * (5 + 6x)) = 0
2x((5 * -9 + 6x * -9) + 2x * (5 + 6x)) = 0
2x((-45 + -54x) + 2x * (5 + 6x)) = 0
2x(-45 + -54x + (5 * 2x + 6x * 2x)) = 0
2x(-45 + -54x + (10x + 12x2)) = 0

Combine like terms: -54x + 10x = -44x
2x(-45 + -44x + 12x2) = 0
(-45 * 2x + -44x * 2x + 12x2 * 2x) = 0
(-90x + -88x2 + 24x3) = 0

Solving
-90x + -88x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-45 + -44x + 12x2) = 0

Factor a trinomial.
2x((-5 + -6x)(9 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 3
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
Solution
x = {0, -0.8333333333, 4.5}

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