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

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Solution for 3x(2x+1)(2x+5)=0 equation:


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

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

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

Multiply (1 + 2x) * (5 + 2x)
3x(1(5 + 2x) + 2x * (5 + 2x)) = 0
3x((5 * 1 + 2x * 1) + 2x * (5 + 2x)) = 0
3x((5 + 2x) + 2x * (5 + 2x)) = 0
3x(5 + 2x + (5 * 2x + 2x * 2x)) = 0
3x(5 + 2x + (10x + 4x2)) = 0

Combine like terms: 2x + 10x = 12x
3x(5 + 12x + 4x2) = 0
(5 * 3x + 12x * 3x + 4x2 * 3x) = 0
(15x + 36x2 + 12x3) = 0

Solving
15x + 36x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(5 + 12x + 4x2) = 0

Factor a trinomial.
3x((5 + 2x)(1 + 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -2.5, -0.5}

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