5x(4x+1)(3x-7)=0

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Solution for 5x(4x+1)(3x-7)=0 equation: 


Simplifying
5x(4x + 1)(3x + -7) = 0

Reorder the terms:
5x(1 + 4x)(3x + -7) = 0

Reorder the terms:
5x(1 + 4x)(-7 + 3x) = 0

Multiply (1 + 4x) * (-7 + 3x)
5x(1(-7 + 3x) + 4x * (-7 + 3x)) = 0
5x((-7 * 1 + 3x * 1) + 4x * (-7 + 3x)) = 0
5x((-7 + 3x) + 4x * (-7 + 3x)) = 0
5x(-7 + 3x + (-7 * 4x + 3x * 4x)) = 0
5x(-7 + 3x + (-28x + 12x2)) = 0

Combine like terms: 3x + -28x = -25x
5x(-7 + -25x + 12x2) = 0
(-7 * 5x + -25x * 5x + 12x2 * 5x) = 0
(-35x + -125x2 + 60x3) = 0

Solving
-35x + -125x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-7 + -25x + 12x2) = 0

Factor a trinomial.
5x((-1 + -4x)(7 + -3x)) = 0

Ignore the factor 5.

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 '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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, -0.25, 2.333333333}

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