4x^2-13x+17=3x+2

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Solution for 4x^2-13x+17=3x+2 equation: 


Simplifying
4x2 + -13x + 17 = 3x + 2

Reorder the terms:
17 + -13x + 4x2 = 3x + 2

Reorder the terms:
17 + -13x + 4x2 = 2 + 3x

Solving
17 + -13x + 4x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
17 + -2 + -13x + -3x + 4x2 = 2 + 3x + -2 + -3x

Combine like terms: 17 + -2 = 15
15 + -13x + -3x + 4x2 = 2 + 3x + -2 + -3x

Combine like terms: -13x + -3x = -16x
15 + -16x + 4x2 = 2 + 3x + -2 + -3x

Reorder the terms:
15 + -16x + 4x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
15 + -16x + 4x2 = 0 + 3x + -3x
15 + -16x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
15 + -16x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(5 + -2x) = 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 '(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
Solution
x = {1.5, 2.5}

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