(8x+3)x(4x+7)=

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Solution for (8x+3)x(4x+7)= equation: 


Simplifying
(8x + 3) * x(4x + 7) = 0

Reorder the terms:
(3 + 8x) * x(4x + 7) = 0

Reorder the terms:
(3 + 8x) * x(7 + 4x) = 0

Reorder the terms for easier multiplication:
x(3 + 8x)(7 + 4x) = 0

Multiply (3 + 8x) * (7 + 4x)
x(3(7 + 4x) + 8x * (7 + 4x)) = 0
x((7 * 3 + 4x * 3) + 8x * (7 + 4x)) = 0
x((21 + 12x) + 8x * (7 + 4x)) = 0
x(21 + 12x + (7 * 8x + 4x * 8x)) = 0
x(21 + 12x + (56x + 32x2)) = 0

Combine like terms: 12x + 56x = 68x
x(21 + 68x + 32x2) = 0
(21 * x + 68x * x + 32x2 * x) = 0
(21x + 68x2 + 32x3) = 0

Solving
21x + 68x2 + 32x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(21 + 68x + 32x2) = 0

Factor a trinomial.
x((7 + 4x)(3 + 8x)) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75

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

Simplifying
3 + 8x = 0

Solving
3 + 8x = 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 + 8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x = 0 + -3
8x = 0 + -3

Combine like terms: 0 + -3 = -3
8x = -3

Divide each side by '8'.
x = -0.375

Simplifying
x = -0.375
Solution
x = {0, -1.75, -0.375}

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