(9x+2)2(x)(x)(-5x-3)=0

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Solution for (9x+2)2(x)(x)(-5x-3)=0 equation: 


Simplifying
(9x + 2) * 2(x)(x)(-5x + -3) = 0

Reorder the terms:
(2 + 9x) * 2(x)(x)(-5x + -3) = 0

Reorder the terms:
(2 + 9x) * 2x * x(-3 + -5x) = 0

Reorder the terms for easier multiplication:
2x * x(2 + 9x)(-3 + -5x) = 0

Multiply x * x
2x2(2 + 9x)(-3 + -5x) = 0

Multiply (2 + 9x) * (-3 + -5x)
2x2(2(-3 + -5x) + 9x * (-3 + -5x)) = 0
2x2((-3 * 2 + -5x * 2) + 9x * (-3 + -5x)) = 0
2x2((-6 + -10x) + 9x * (-3 + -5x)) = 0
2x2(-6 + -10x + (-3 * 9x + -5x * 9x)) = 0
2x2(-6 + -10x + (-27x + -45x2)) = 0

Combine like terms: -10x + -27x = -37x
2x2(-6 + -37x + -45x2) = 0
(-6 * 2x2 + -37x * 2x2 + -45x2 * 2x2) = 0
(-12x2 + -74x3 + -90x4) = 0

Solving
-12x2 + -74x3 + -90x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2x2'.
-2x2(6 + 37x + 45x2) = 0

Factor a trinomial.
-2x2((3 + 5x)(2 + 9x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 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 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 3
Set the factor '(2 + 9x)' equal to zero and attempt to solve:

Simplifying
2 + 9x = 0

Solving
2 + 9x = 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 + 9x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9x = 0 + -2
9x = 0 + -2

Combine like terms: 0 + -2 = -2
9x = -2

Divide each side by '9'.
x = -0.2222222222

Simplifying
x = -0.2222222222
Solution
x = {0, -0.6, -0.2222222222}

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