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

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


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

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

Combine like terms: 6x + -17x = -11x
13 + -11x = 20x2 + -32

Reorder the terms:
13 + -11x = -32 + 20x2

Solving
13 + -11x = -32 + 20x2

Solving for variable 'x'.

Reorder the terms:
13 + 32 + -11x + -20x2 = -32 + 20x2 + 32 + -20x2

Combine like terms: 13 + 32 = 45
45 + -11x + -20x2 = -32 + 20x2 + 32 + -20x2

Reorder the terms:
45 + -11x + -20x2 = -32 + 32 + 20x2 + -20x2

Combine like terms: -32 + 32 = 0
45 + -11x + -20x2 = 0 + 20x2 + -20x2
45 + -11x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
45 + -11x + -20x2 = 0

Factor a trinomial.
(5 + -4x)(9 + 5x) = 0


Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 2
Set the factor '(9 + 5x)' equal to zero and attempt to solve:

Simplifying
9 + 5x = 0

Solving
9 + 5x = 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 + 5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5x = 0 + -9
5x = 0 + -9

Combine like terms: 0 + -9 = -9
5x = -9

Divide each side by '5'.
x = -1.8

Simplifying
x = -1.8
Solution
x = {1.25, -1.8}

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