2(3x+1)(2x-9)=0

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Solution for 2(3x+1)(2x-9)=0 equation: 


Simplifying
2(3x + 1)(2x + -9) = 0

Reorder the terms:
2(1 + 3x)(2x + -9) = 0

Reorder the terms:
2(1 + 3x)(-9 + 2x) = 0

Multiply (1 + 3x) * (-9 + 2x)
2(1(-9 + 2x) + 3x * (-9 + 2x)) = 0
2((-9 * 1 + 2x * 1) + 3x * (-9 + 2x)) = 0
2((-9 + 2x) + 3x * (-9 + 2x)) = 0
2(-9 + 2x + (-9 * 3x + 2x * 3x)) = 0
2(-9 + 2x + (-27x + 6x2)) = 0

Combine like terms: 2x + -27x = -25x
2(-9 + -25x + 6x2) = 0
(-9 * 2 + -25x * 2 + 6x2 * 2) = 0
(-18 + -50x + 12x2) = 0

Solving
-18 + -50x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -25x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
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 = {-0.3333333333, 4.5}

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