3x^2+6x-17=13-7x

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Solution for 3x^2+6x-17=13-7x equation: 


Simplifying
3x2 + 6x + -17 = 13 + -7x

Reorder the terms:
-17 + 6x + 3x2 = 13 + -7x

Solving
-17 + 6x + 3x2 = 13 + -7x

Solving for variable 'x'.

Reorder the terms:
-17 + -13 + 6x + 7x + 3x2 = 13 + -7x + -13 + 7x

Combine like terms: -17 + -13 = -30
-30 + 6x + 7x + 3x2 = 13 + -7x + -13 + 7x

Combine like terms: 6x + 7x = 13x
-30 + 13x + 3x2 = 13 + -7x + -13 + 7x

Reorder the terms:
-30 + 13x + 3x2 = 13 + -13 + -7x + 7x

Combine like terms: 13 + -13 = 0
-30 + 13x + 3x2 = 0 + -7x + 7x
-30 + 13x + 3x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-30 + 13x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 1.666666667}

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