3x^2-8x=20+3x

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Solution for 3x^2-8x=20+3x equation:


Simplifying
3x2 + -8x = 20 + 3x

Reorder the terms:
-8x + 3x2 = 20 + 3x

Solving
-8x + 3x2 = 20 + 3x

Solving for variable 'x'.

Reorder the terms:
-20 + -8x + -3x + 3x2 = 20 + 3x + -20 + -3x

Combine like terms: -8x + -3x = -11x
-20 + -11x + 3x2 = 20 + 3x + -20 + -3x

Reorder the terms:
-20 + -11x + 3x2 = 20 + -20 + 3x + -3x

Combine like terms: 20 + -20 = 0
-20 + -11x + 3x2 = 0 + 3x + -3x
-20 + -11x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-20 + -11x + 3x2 = 0

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

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

Subproblem 2

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

Solution

x = {-1.333333333, 5}

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