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

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


Simplifying
x(7 + -1x)(x + -5) = 0

Reorder the terms:
x(7 + -1x)(-5 + x) = 0

Multiply (7 + -1x) * (-5 + x)
x(7(-5 + x) + -1x * (-5 + x)) = 0
x((-5 * 7 + x * 7) + -1x * (-5 + x)) = 0
x((-35 + 7x) + -1x * (-5 + x)) = 0
x(-35 + 7x + (-5 * -1x + x * -1x)) = 0
x(-35 + 7x + (5x + -1x2)) = 0

Combine like terms: 7x + 5x = 12x
x(-35 + 12x + -1x2) = 0
(-35 * x + 12x * x + -1x2 * x) = 0
(-35x + 12x2 + -1x3) = 0

Solving
-35x + 12x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + 12x + -1x2) = 0

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


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 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

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

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

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

Simplifying
x = 7

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, 7, 5}

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