3x(4+x)=14+x

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Solution for 3x(4+x)=14+x equation: 


Simplifying
3x(4 + x) = 14 + x
(4 * 3x + x * 3x) = 14 + x
(12x + 3x2) = 14 + x

Solving
12x + 3x2 = 14 + x

Solving for variable 'x'.

Reorder the terms:
-14 + 12x + -1x + 3x2 = 14 + x + -14 + -1x

Combine like terms: 12x + -1x = 11x
-14 + 11x + 3x2 = 14 + x + -14 + -1x

Reorder the terms:
-14 + 11x + 3x2 = 14 + -14 + x + -1x

Combine like terms: 14 + -14 = 0
-14 + 11x + 3x2 = 0 + x + -1x
-14 + 11x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-14 + 11x + 3x2 = 0

Factor a trinomial.
(-14 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-14 + -3x)' equal to zero and attempt to solve:

Simplifying
-14 + -3x = 0

Solving
-14 + -3x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -3x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3x = 0 + 14
-3x = 0 + 14

Combine like terms: 0 + 14 = 14
-3x = 14

Divide each side by '-3'.
x = -4.666666667

Simplifying
x = -4.666666667

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-4.666666667, 1}

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