(2x^2-3x)(9x+3)=

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


Simplifying
(2x2 + -3x)(9x + 3) = 0

Reorder the terms:
(-3x + 2x2)(9x + 3) = 0

Reorder the terms:
(-3x + 2x2)(3 + 9x) = 0

Multiply (-3x + 2x2) * (3 + 9x)
(-3x * (3 + 9x) + 2x2 * (3 + 9x)) = 0
((3 * -3x + 9x * -3x) + 2x2 * (3 + 9x)) = 0
((-9x + -27x2) + 2x2 * (3 + 9x)) = 0
(-9x + -27x2 + (3 * 2x2 + 9x * 2x2)) = 0
(-9x + -27x2 + (6x2 + 18x3)) = 0

Combine like terms: -27x2 + 6x2 = -21x2
(-9x + -21x2 + 18x3) = 0

Solving
-9x + -21x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-3 + -7x + 6x2) = 0

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

Ignore the factor 3.

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 '(-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 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -0.3333333333, 1.5}

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