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

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


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

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

Multiply (-7 + x) * (5 + -2x)
x(-7(5 + -2x) + x(5 + -2x)) = 0
x((5 * -7 + -2x * -7) + x(5 + -2x)) = 0
x((-35 + 14x) + x(5 + -2x)) = 0
x(-35 + 14x + (5 * x + -2x * x)) = 0
x(-35 + 14x + (5x + -2x2)) = 0

Combine like terms: 14x + 5x = 19x
x(-35 + 19x + -2x2) = 0
(-35 * x + 19x * x + -2x2 * x) = 0
(-35x + 19x2 + -2x3) = 0

Solving
-35x + 19x2 + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + 19x + -2x2) = 0

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 7, 2.5}

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