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

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


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

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

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

Multiply (9 + 2x) * (-3 + 9x)
(9(-3 + 9x) + 2x * (-3 + 9x)) = 0
((-3 * 9 + 9x * 9) + 2x * (-3 + 9x)) = 0
((-27 + 81x) + 2x * (-3 + 9x)) = 0
(-27 + 81x + (-3 * 2x + 9x * 2x)) = 0
(-27 + 81x + (-6x + 18x2)) = 0

Combine like terms: 81x + -6x = 75x
(-27 + 75x + 18x2) = 0

Solving
-27 + 75x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 25x + 6x2) = 0

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

Ignore the factor 3.

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 '(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
Solution
x = {-4.5, 0.3333333333}

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