3x(x+2)=5-8x

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Solution for 3x(x+2)=5-8x equation:


Simplifying
3x(x + 2) = 5 + -8x

Reorder the terms:
3x(2 + x) = 5 + -8x
(2 * 3x + x * 3x) = 5 + -8x
(6x + 3x2) = 5 + -8x

Solving
6x + 3x2 = 5 + -8x

Solving for variable 'x'.

Reorder the terms:
-5 + 6x + 8x + 3x2 = 5 + -8x + -5 + 8x

Combine like terms: 6x + 8x = 14x
-5 + 14x + 3x2 = 5 + -8x + -5 + 8x

Reorder the terms:
-5 + 14x + 3x2 = 5 + -5 + -8x + 8x

Combine like terms: 5 + -5 = 0
-5 + 14x + 3x2 = 0 + -8x + 8x
-5 + 14x + 3x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-5 + 14x + 3x2 = 0

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

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {-5, 0.3333333333}

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