14x(2x-11)(4x-14)=0

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Solution for 14x(2x-11)(4x-14)=0 equation: 


Simplifying
14x(2x + -11)(4x + -14) = 0

Reorder the terms:
14x(-11 + 2x)(4x + -14) = 0

Reorder the terms:
14x(-11 + 2x)(-14 + 4x) = 0

Multiply (-11 + 2x) * (-14 + 4x)
14x(-11(-14 + 4x) + 2x * (-14 + 4x)) = 0
14x((-14 * -11 + 4x * -11) + 2x * (-14 + 4x)) = 0
14x((154 + -44x) + 2x * (-14 + 4x)) = 0
14x(154 + -44x + (-14 * 2x + 4x * 2x)) = 0
14x(154 + -44x + (-28x + 8x2)) = 0

Combine like terms: -44x + -28x = -72x
14x(154 + -72x + 8x2) = 0
(154 * 14x + -72x * 14x + 8x2 * 14x) = 0
(2156x + -1008x2 + 112x3) = 0

Solving
2156x + -1008x2 + 112x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '28x'.
28x(77 + -36x + 4x2) = 0

Factor a trinomial.
28x((7 + -2x)(11 + -2x)) = 0

Ignore the factor 28.

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 + -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

Subproblem 3
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {0, 3.5, 5.5}

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