3x^2-3x+17=5x^2-3

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Solution for 3x^2-3x+17=5x^2-3 equation: 


Simplifying
3x2 + -3x + 17 = 5x2 + -3

Reorder the terms:
17 + -3x + 3x2 = 5x2 + -3

Reorder the terms:
17 + -3x + 3x2 = -3 + 5x2

Solving
17 + -3x + 3x2 = -3 + 5x2

Solving for variable 'x'.

Reorder the terms:
17 + 3 + -3x + 3x2 + -5x2 = -3 + 5x2 + 3 + -5x2

Combine like terms: 17 + 3 = 20
20 + -3x + 3x2 + -5x2 = -3 + 5x2 + 3 + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
20 + -3x + -2x2 = -3 + 5x2 + 3 + -5x2

Reorder the terms:
20 + -3x + -2x2 = -3 + 3 + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
20 + -3x + -2x2 = 0 + 5x2 + -5x2
20 + -3x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
20 + -3x + -2x2 = 0

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


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {2.5, -4}

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