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

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


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

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

Multiply (5 + -2x) * (7 + -2x)
x(5(7 + -2x) + -2x * (7 + -2x)) = 0
x((7 * 5 + -2x * 5) + -2x * (7 + -2x)) = 0
x((35 + -10x) + -2x * (7 + -2x)) = 0
x(35 + -10x + (7 * -2x + -2x * -2x)) = 0
x(35 + -10x + (-14x + 4x2)) = 0

Combine like terms: -10x + -14x = -24x
x(35 + -24x + 4x2) = 0
(35 * x + -24x * x + 4x2 * x) = 0
(35x + -24x2 + 4x3) = 0

Solving
35x + -24x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(35 + -24x + 4x2) = 0

Factor a trinomial.
x((5 + -2x)(7 + -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 '(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

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, 2.5, 3.5}

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