(3x+7)(4x-7)(9874x)=0

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Solution for (3x+7)(4x-7)(9874x)=0 equation: 


Simplifying
(3x + 7)(4x + -7)(9874x) = 0

Reorder the terms:
(7 + 3x)(4x + -7)(9874x) = 0

Reorder the terms:
(7 + 3x)(-7 + 4x)(9874x) = 0

Remove parenthesis around (9874x)
(7 + 3x)(-7 + 4x) * 9874x = 0

Reorder the terms for easier multiplication:
9874x(7 + 3x)(-7 + 4x) = 0

Multiply (7 + 3x) * (-7 + 4x)
9874x(7(-7 + 4x) + 3x * (-7 + 4x)) = 0
9874x((-7 * 7 + 4x * 7) + 3x * (-7 + 4x)) = 0
9874x((-49 + 28x) + 3x * (-7 + 4x)) = 0
9874x(-49 + 28x + (-7 * 3x + 4x * 3x)) = 0
9874x(-49 + 28x + (-21x + 12x2)) = 0

Combine like terms: 28x + -21x = 7x
9874x(-49 + 7x + 12x2) = 0
(-49 * 9874x + 7x * 9874x + 12x2 * 9874x) = 0
(-483826x + 69118x2 + 118488x3) = 0

Solving
-483826x + 69118x2 + 118488x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9874x'.
9874x(-49 + 7x + 12x2) = 0

Factor a trinomial.
9874x((-7 + -3x)(7 + -4x)) = 0

Ignore the factor 9874.

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 + -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

Subproblem 3
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
Solution
x = {0, -2.333333333, 1.75}

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