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

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


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

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

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

Multiply (7 + x) * (-3 + 5x)
3x(7(-3 + 5x) + x(-3 + 5x)) = 0
3x((-3 * 7 + 5x * 7) + x(-3 + 5x)) = 0
3x((-21 + 35x) + x(-3 + 5x)) = 0
3x(-21 + 35x + (-3 * x + 5x * x)) = 0
3x(-21 + 35x + (-3x + 5x2)) = 0

Combine like terms: 35x + -3x = 32x
3x(-21 + 32x + 5x2) = 0
(-21 * 3x + 32x * 3x + 5x2 * 3x) = 0
(-63x + 96x2 + 15x3) = 0

Solving
-63x + 96x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-21 + 32x + 5x2) = 0

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

Ignore the factor 3.

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 '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, -7, 0.6}

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