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

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


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

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

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

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

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

Combine like terms: -4x + -7x = -11x
x(14 + -11x + 2x2) = 0
(14 * x + -11x * x + 2x2 * x) = 0
(14x + -11x2 + 2x3) = 0

Solving
14x + -11x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(14 + -11x + 2x2) = 0

Factor a trinomial.
x((2 + -1x)(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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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, 3.5}

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