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

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


Simplifying
x(2x + 7)(3 + -1x) = 0

Reorder the terms:
x(7 + 2x)(3 + -1x) = 0

Multiply (7 + 2x) * (3 + -1x)
x(7(3 + -1x) + 2x * (3 + -1x)) = 0
x((3 * 7 + -1x * 7) + 2x * (3 + -1x)) = 0
x((21 + -7x) + 2x * (3 + -1x)) = 0
x(21 + -7x + (3 * 2x + -1x * 2x)) = 0
x(21 + -7x + (6x + -2x2)) = 0

Combine like terms: -7x + 6x = -1x
x(21 + -1x + -2x2) = 0
(21 * x + -1x * x + -2x2 * x) = 0
(21x + -1x2 + -2x3) = 0

Solving
21x + -1x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(21 + -1x + -2x2) = 0

Factor a trinomial.
x((3 + -1x)(7 + 2x)) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 3
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
Solution
x = {0, 3, -3.5}

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