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

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


Simplifying
-5x(x + -7)(3x + 2) = 0

Reorder the terms:
-5x(-7 + x)(3x + 2) = 0

Reorder the terms:
-5x(-7 + x)(2 + 3x) = 0

Multiply (-7 + x) * (2 + 3x)
-5x(-7(2 + 3x) + x(2 + 3x)) = 0
-5x((2 * -7 + 3x * -7) + x(2 + 3x)) = 0
-5x((-14 + -21x) + x(2 + 3x)) = 0
-5x(-14 + -21x + (2 * x + 3x * x)) = 0
-5x(-14 + -21x + (2x + 3x2)) = 0

Combine like terms: -21x + 2x = -19x
-5x(-14 + -19x + 3x2) = 0
(-14 * -5x + -19x * -5x + 3x2 * -5x) = 0
(70x + 95x2 + -15x3) = 0

Solving
70x + 95x2 + -15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(14 + 19x + -3x2) = 0

Factor a trinomial.
5x((7 + -1x)(2 + 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 3
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, 7, -0.6666666667}

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