(3x+16)x(7x+8)=

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Solution for (3x+16)x(7x+8)= equation: 


Simplifying
(3x + 16) * x(7x + 8) = 0

Reorder the terms:
(16 + 3x) * x(7x + 8) = 0

Reorder the terms:
(16 + 3x) * x(8 + 7x) = 0

Reorder the terms for easier multiplication:
x(16 + 3x)(8 + 7x) = 0

Multiply (16 + 3x) * (8 + 7x)
x(16(8 + 7x) + 3x * (8 + 7x)) = 0
x((8 * 16 + 7x * 16) + 3x * (8 + 7x)) = 0
x((128 + 112x) + 3x * (8 + 7x)) = 0
x(128 + 112x + (8 * 3x + 7x * 3x)) = 0
x(128 + 112x + (24x + 21x2)) = 0

Combine like terms: 112x + 24x = 136x
x(128 + 136x + 21x2) = 0
(128 * x + 136x * x + 21x2 * x) = 0
(128x + 136x2 + 21x3) = 0

Solving
128x + 136x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(128 + 136x + 21x2) = 0

Factor a trinomial.
x((16 + 3x)(8 + 7x)) = 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 '(16 + 3x)' equal to zero and attempt to solve:

Simplifying
16 + 3x = 0

Solving
16 + 3x = 0

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

Add '-16' to each side of the equation.
16 + -16 + 3x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 3x = 0 + -16
3x = 0 + -16

Combine like terms: 0 + -16 = -16
3x = -16

Divide each side by '3'.
x = -5.333333333

Simplifying
x = -5.333333333

Subproblem 3
Set the factor '(8 + 7x)' equal to zero and attempt to solve:

Simplifying
8 + 7x = 0

Solving
8 + 7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7x = 0 + -8
7x = 0 + -8

Combine like terms: 0 + -8 = -8
7x = -8

Divide each side by '7'.
x = -1.142857143

Simplifying
x = -1.142857143
Solution
x = {0, -5.333333333, -1.142857143}

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