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

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


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

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

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

Solving
30x + 22x2 + 4x3 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

Subproblem 3
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
Solution
x = {0, -3, -2.5}

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