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

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


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

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

Multiply (-5 + x) * (7 + -2x)
3x(-5(7 + -2x) + x(7 + -2x)) = 0
3x((7 * -5 + -2x * -5) + x(7 + -2x)) = 0
3x((-35 + 10x) + x(7 + -2x)) = 0
3x(-35 + 10x + (7 * x + -2x * x)) = 0
3x(-35 + 10x + (7x + -2x2)) = 0

Combine like terms: 10x + 7x = 17x
3x(-35 + 17x + -2x2) = 0
(-35 * 3x + 17x * 3x + -2x2 * 3x) = 0
(-105x + 51x2 + -6x3) = 0

Solving
-105x + 51x2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-35 + 17x + -2x2) = 0

Factor a trinomial.
3x((-5 + x)(7 + -2x)) = 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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 3
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 5, 3.5}

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