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

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


Simplifying
-2x + 17 = 2x2 + 3x + 5

Reorder the terms:
17 + -2x = 2x2 + 3x + 5

Reorder the terms:
17 + -2x = 5 + 3x + 2x2

Solving
17 + -2x = 5 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
17 + -5 + -2x + -3x + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2

Combine like terms: 17 + -5 = 12
12 + -2x + -3x + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2

Combine like terms: -2x + -3x = -5x
12 + -5x + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2

Reorder the terms:
12 + -5x + -2x2 = 5 + -5 + 3x + -3x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
12 + -5x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
12 + -5x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
12 + -5x + -2x2 = 0 + 2x2 + -2x2
12 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -5x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(4 + x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, -4}

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