x(2x+7)(3x+5)=0

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Solution for x(2x+7)(3x+5)=0 equation: 


Simplifying
x(2x + 7)(3x + 5) = 0

Reorder the terms:
x(7 + 2x)(3x + 5) = 0

Reorder the terms:
x(7 + 2x)(5 + 3x) = 0

Multiply (7 + 2x) * (5 + 3x)
x(7(5 + 3x) + 2x * (5 + 3x)) = 0
x((5 * 7 + 3x * 7) + 2x * (5 + 3x)) = 0
x((35 + 21x) + 2x * (5 + 3x)) = 0
x(35 + 21x + (5 * 2x + 3x * 2x)) = 0
x(35 + 21x + (10x + 6x2)) = 0

Combine like terms: 21x + 10x = 31x
x(35 + 31x + 6x2) = 0
(35 * x + 31x * x + 6x2 * x) = 0
(35x + 31x2 + 6x3) = 0

Solving
35x + 31x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(35 + 31x + 6x2) = 0

Factor a trinomial.
x((7 + 2x)(5 + 3x)) = 0


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 '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

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

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

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
5 + 3x = 0

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

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

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

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0, -3.5, -1.666666667}

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