3x(7x+2)(9x+10)=0

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Solution for 3x(7x+2)(9x+10)=0 equation: 


Simplifying
3x(7x + 2)(9x + 10) = 0

Reorder the terms:
3x(2 + 7x)(9x + 10) = 0

Reorder the terms:
3x(2 + 7x)(10 + 9x) = 0

Multiply (2 + 7x) * (10 + 9x)
3x(2(10 + 9x) + 7x * (10 + 9x)) = 0
3x((10 * 2 + 9x * 2) + 7x * (10 + 9x)) = 0
3x((20 + 18x) + 7x * (10 + 9x)) = 0
3x(20 + 18x + (10 * 7x + 9x * 7x)) = 0
3x(20 + 18x + (70x + 63x2)) = 0

Combine like terms: 18x + 70x = 88x
3x(20 + 88x + 63x2) = 0
(20 * 3x + 88x * 3x + 63x2 * 3x) = 0
(60x + 264x2 + 189x3) = 0

Solving
60x + 264x2 + 189x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(20 + 88x + 63x2) = 0

Factor a trinomial.
3x((10 + 9x)(2 + 7x)) = 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 '(10 + 9x)' equal to zero and attempt to solve:

Simplifying
10 + 9x = 0

Solving
10 + 9x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 9x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x = 0 + -10
9x = 0 + -10

Combine like terms: 0 + -10 = -10
9x = -10

Divide each side by '9'.
x = -1.111111111

Simplifying
x = -1.111111111

Subproblem 3
Set the factor '(2 + 7x)' equal to zero and attempt to solve:

Simplifying
2 + 7x = 0

Solving
2 + 7x = 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 + 7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x = 0 + -2
7x = 0 + -2

Combine like terms: 0 + -2 = -2
7x = -2

Divide each side by '7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Solution
x = {0, -1.111111111, -0.2857142857}

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