2x(3x+1)(5x+2)=

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Solution for 2x(3x+1)(5x+2)= equation: 


Simplifying
2x(3x + 1)(5x + 2) = 0

Reorder the terms:
2x(1 + 3x)(5x + 2) = 0

Reorder the terms:
2x(1 + 3x)(2 + 5x) = 0

Multiply (1 + 3x) * (2 + 5x)
2x(1(2 + 5x) + 3x * (2 + 5x)) = 0
2x((2 * 1 + 5x * 1) + 3x * (2 + 5x)) = 0
2x((2 + 5x) + 3x * (2 + 5x)) = 0
2x(2 + 5x + (2 * 3x + 5x * 3x)) = 0
2x(2 + 5x + (6x + 15x2)) = 0

Combine like terms: 5x + 6x = 11x
2x(2 + 11x + 15x2) = 0
(2 * 2x + 11x * 2x + 15x2 * 2x) = 0
(4x + 22x2 + 30x3) = 0

Solving
4x + 22x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + 11x + 15x2) = 0

Factor a trinomial.
2x((2 + 5x)(1 + 3x)) = 0

Ignore the factor 2.

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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 3
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 = {0, -0.4, -0.3333333333}

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