x(x-7)(2x-10)=0

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Solution for x(x-7)(2x-10)=0 equation: 


Simplifying
x(x + -7)(2x + -10) = 0

Reorder the terms:
x(-7 + x)(2x + -10) = 0

Reorder the terms:
x(-7 + x)(-10 + 2x) = 0

Multiply (-7 + x) * (-10 + 2x)
x(-7(-10 + 2x) + x(-10 + 2x)) = 0
x((-10 * -7 + 2x * -7) + x(-10 + 2x)) = 0
x((70 + -14x) + x(-10 + 2x)) = 0
x(70 + -14x + (-10 * x + 2x * x)) = 0
x(70 + -14x + (-10x + 2x2)) = 0

Combine like terms: -14x + -10x = -24x
x(70 + -24x + 2x2) = 0
(70 * x + -24x * x + 2x2 * x) = 0
(70x + -24x2 + 2x3) = 0

Solving
70x + -24x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(35 + -12x + x2) = 0

Factor a trinomial.
2x((5 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

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 + -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

Subproblem 3
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
Solution
x = {0, 5, 7}

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