6x(4x-7)(x+5)=0

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Solution for 6x(4x-7)(x+5)=0 equation: 


Simplifying
6x(4x + -7)(x + 5) = 0

Reorder the terms:
6x(-7 + 4x)(x + 5) = 0

Reorder the terms:
6x(-7 + 4x)(5 + x) = 0

Multiply (-7 + 4x) * (5 + x)
6x(-7(5 + x) + 4x * (5 + x)) = 0
6x((5 * -7 + x * -7) + 4x * (5 + x)) = 0
6x((-35 + -7x) + 4x * (5 + x)) = 0
6x(-35 + -7x + (5 * 4x + x * 4x)) = 0
6x(-35 + -7x + (20x + 4x2)) = 0

Combine like terms: -7x + 20x = 13x
6x(-35 + 13x + 4x2) = 0
(-35 * 6x + 13x * 6x + 4x2 * 6x) = 0
(-210x + 78x2 + 24x3) = 0

Solving
-210x + 78x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-35 + 13x + 4x2) = 0

Factor a trinomial.
6x((-5 + -1x)(7 + -4x)) = 0

Ignore the factor 6.

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 '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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, -5, 1.75}

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