3x+x(x+2)=6

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Solution for 3x+x(x+2)=6 equation:


Simplifying
3x + x(x + 2) = 6

Reorder the terms:
3x + x(2 + x) = 6
3x + (2 * x + x * x) = 6
3x + (2x + x2) = 6

Combine like terms: 3x + 2x = 5x
5x + x2 = 6

Solving
5x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

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 = {-6, 1}

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