6x^2-17x+13=20x-32

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Solution for 6x^2-17x+13=20x-32 equation: 


Simplifying
6x2 + -17x + 13 = 20x + -32

Reorder the terms:
13 + -17x + 6x2 = 20x + -32

Reorder the terms:
13 + -17x + 6x2 = -32 + 20x

Solving
13 + -17x + 6x2 = -32 + 20x

Solving for variable 'x'.

Reorder the terms:
13 + 32 + -17x + -20x + 6x2 = -32 + 20x + 32 + -20x

Combine like terms: 13 + 32 = 45
45 + -17x + -20x + 6x2 = -32 + 20x + 32 + -20x

Combine like terms: -17x + -20x = -37x
45 + -37x + 6x2 = -32 + 20x + 32 + -20x

Reorder the terms:
45 + -37x + 6x2 = -32 + 32 + 20x + -20x

Combine like terms: -32 + 32 = 0
45 + -37x + 6x2 = 0 + 20x + -20x
45 + -37x + 6x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
45 + -37x + 6x2 = 0

Factor a trinomial.
(5 + -3x)(9 + -2x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1.666666667, 4.5}

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