6x^2=20x^2-45+17x

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Solution for 6x^2=20x^2-45+17x equation: 


Simplifying
6x2 = 20x2 + -45 + 17x

Reorder the terms:
6x2 = -45 + 17x + 20x2

Solving
6x2 = -45 + 17x + 20x2

Solving for variable 'x'.

Reorder the terms:
45 + -17x + 6x2 + -20x2 = -45 + 17x + 20x2 + 45 + -17x + -20x2

Combine like terms: 6x2 + -20x2 = -14x2
45 + -17x + -14x2 = -45 + 17x + 20x2 + 45 + -17x + -20x2

Reorder the terms:
45 + -17x + -14x2 = -45 + 45 + 17x + -17x + 20x2 + -20x2

Combine like terms: -45 + 45 = 0
45 + -17x + -14x2 = 0 + 17x + -17x + 20x2 + -20x2
45 + -17x + -14x2 = 17x + -17x + 20x2 + -20x2

Combine like terms: 17x + -17x = 0
45 + -17x + -14x2 = 0 + 20x2 + -20x2
45 + -17x + -14x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
45 + -17x + -14x2 = 0

Factor a trinomial.
(9 + -7x)(5 + 2x) = 0


Subproblem 1
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 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 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286

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 = {1.285714286, -2.5}

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