-3x(x-7)(-4x+11)=0

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Solution for -3x(x-7)(-4x+11)=0 equation: 


Simplifying
-3x(x + -7)(-4x + 11) = 0

Reorder the terms:
-3x(-7 + x)(-4x + 11) = 0

Reorder the terms:
-3x(-7 + x)(11 + -4x) = 0

Multiply (-7 + x) * (11 + -4x)
-3x(-7(11 + -4x) + x(11 + -4x)) = 0
-3x((11 * -7 + -4x * -7) + x(11 + -4x)) = 0
-3x((-77 + 28x) + x(11 + -4x)) = 0
-3x(-77 + 28x + (11 * x + -4x * x)) = 0
-3x(-77 + 28x + (11x + -4x2)) = 0

Combine like terms: 28x + 11x = 39x
-3x(-77 + 39x + -4x2) = 0
(-77 * -3x + 39x * -3x + -4x2 * -3x) = 0
(231x + -117x2 + 12x3) = 0

Solving
231x + -117x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(77 + -39x + 4x2) = 0

Factor a trinomial.
3x((11 + -4x)(7 + -1x)) = 0

Ignore the factor 3.

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 '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 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 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75

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, 2.75, 7}

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