4x^2-13x+17=6x+5

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Solution for 4x^2-13x+17=6x+5 equation: 


Simplifying
4x2 + -13x + 17 = 6x + 5

Reorder the terms:
17 + -13x + 4x2 = 6x + 5

Reorder the terms:
17 + -13x + 4x2 = 5 + 6x

Solving
17 + -13x + 4x2 = 5 + 6x

Solving for variable 'x'.

Reorder the terms:
17 + -5 + -13x + -6x + 4x2 = 5 + 6x + -5 + -6x

Combine like terms: 17 + -5 = 12
12 + -13x + -6x + 4x2 = 5 + 6x + -5 + -6x

Combine like terms: -13x + -6x = -19x
12 + -19x + 4x2 = 5 + 6x + -5 + -6x

Reorder the terms:
12 + -19x + 4x2 = 5 + -5 + 6x + -6x

Combine like terms: 5 + -5 = 0
12 + -19x + 4x2 = 0 + 6x + -6x
12 + -19x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -19x + 4x2 = 0

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


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.75, 4}

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