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

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


Simplifying
(3x + 7)(x2 + 5x + 2x) = 0

Reorder the terms:
(7 + 3x)(x2 + 5x + 2x) = 0

Reorder the terms:
(7 + 3x)(5x + 2x + x2) = 0

Combine like terms: 5x + 2x = 7x
(7 + 3x)(7x + x2) = 0

Multiply (7 + 3x) * (7x + x2)
(7(7x + x2) + 3x * (7x + x2)) = 0
((7x * 7 + x2 * 7) + 3x * (7x + x2)) = 0
((49x + 7x2) + 3x * (7x + x2)) = 0
(49x + 7x2 + (7x * 3x + x2 * 3x)) = 0
(49x + 7x2 + (21x2 + 3x3)) = 0

Combine like terms: 7x2 + 21x2 = 28x2
(49x + 28x2 + 3x3) = 0

Solving
49x + 28x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(49 + 28x + 3x2) = 0

Factor a trinomial.
x((7 + x)(7 + 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 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7

Subproblem 3
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0, -7, -2.333333333}

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