3x(x+2)=20-x

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Solution for 3x(x+2)=20-x equation:


Simplifying
3x(x + 2) = 20 + -1x

Reorder the terms:
3x(2 + x) = 20 + -1x
(2 * 3x + x * 3x) = 20 + -1x
(6x + 3x2) = 20 + -1x

Solving
6x + 3x2 = 20 + -1x

Solving for variable 'x'.

Reorder the terms:
-20 + 6x + x + 3x2 = 20 + -1x + -20 + x

Combine like terms: 6x + x = 7x
-20 + 7x + 3x2 = 20 + -1x + -20 + x

Reorder the terms:
-20 + 7x + 3x2 = 20 + -20 + -1x + x

Combine like terms: 20 + -20 = 0
-20 + 7x + 3x2 = 0 + -1x + x
-20 + 7x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
-20 + 7x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -3x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-4, 1.666666667}

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