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

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


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

Reorder the terms:
3x(-4 + x) + 11(x + -4) = 0
(-4 * 3x + x * 3x) + 11(x + -4) = 0
(-12x + 3x2) + 11(x + -4) = 0

Reorder the terms:
-12x + 3x2 + 11(-4 + x) = 0
-12x + 3x2 + (-4 * 11 + x * 11) = 0
-12x + 3x2 + (-44 + 11x) = 0

Reorder the terms:
-44 + -12x + 11x + 3x2 = 0

Combine like terms: -12x + 11x = -1x
-44 + -1x + 3x2 = 0

Solving
-44 + -1x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 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 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3.666666667, 4}

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