6x^2(x-5)(3x+7)=0

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Solution for 6x^2(x-5)(3x+7)=0 equation: 


Simplifying
6x2(x + -5)(3x + 7) = 0

Reorder the terms:
6x2(-5 + x)(3x + 7) = 0

Reorder the terms:
6x2(-5 + x)(7 + 3x) = 0

Multiply (-5 + x) * (7 + 3x)
6x2(-5(7 + 3x) + x(7 + 3x)) = 0
6x2((7 * -5 + 3x * -5) + x(7 + 3x)) = 0
6x2((-35 + -15x) + x(7 + 3x)) = 0
6x2(-35 + -15x + (7 * x + 3x * x)) = 0
6x2(-35 + -15x + (7x + 3x2)) = 0

Combine like terms: -15x + 7x = -8x
6x2(-35 + -8x + 3x2) = 0
(-35 * 6x2 + -8x * 6x2 + 3x2 * 6x2) = 0
(-210x2 + -48x3 + 18x4) = 0

Solving
-210x2 + -48x3 + 18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-35 + -8x + 3x2) = 0

Factor a trinomial.
6x2((-7 + -3x)(5 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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 '(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
Solution
x = {0, -2.333333333, 5}

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