3x^2-17x=-2x^2-3x-8

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Solution for 3x^2-17x=-2x^2-3x-8 equation:


Simplifying
3x2 + -17x = -2x2 + -3x + -8

Reorder the terms:
-17x + 3x2 = -2x2 + -3x + -8

Reorder the terms:
-17x + 3x2 = -8 + -3x + -2x2

Solving
-17x + 3x2 = -8 + -3x + -2x2

Solving for variable 'x'.

Reorder the terms:
8 + -17x + 3x + 3x2 + 2x2 = -8 + -3x + -2x2 + 8 + 3x + 2x2

Combine like terms: -17x + 3x = -14x
8 + -14x + 3x2 + 2x2 = -8 + -3x + -2x2 + 8 + 3x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
8 + -14x + 5x2 = -8 + -3x + -2x2 + 8 + 3x + 2x2

Reorder the terms:
8 + -14x + 5x2 = -8 + 8 + -3x + 3x + -2x2 + 2x2

Combine like terms: -8 + 8 = 0
8 + -14x + 5x2 = 0 + -3x + 3x + -2x2 + 2x2
8 + -14x + 5x2 = -3x + 3x + -2x2 + 2x2

Combine like terms: -3x + 3x = 0
8 + -14x + 5x2 = 0 + -2x2 + 2x2
8 + -14x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
8 + -14x + 5x2 = 0

Factor a trinomial.
(4 + -5x)(2 + -1x) = 0

Subproblem 1

Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0.8, 2}

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