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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