3x^2+7x-15=17-13x

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Solution for 3x^2+7x-15=17-13x equation: 


Simplifying
3x2 + 7x + -15 = 17 + -13x

Reorder the terms:
-15 + 7x + 3x2 = 17 + -13x

Solving
-15 + 7x + 3x2 = 17 + -13x

Solving for variable 'x'.

Reorder the terms:
-15 + -17 + 7x + 13x + 3x2 = 17 + -13x + -17 + 13x

Combine like terms: -15 + -17 = -32
-32 + 7x + 13x + 3x2 = 17 + -13x + -17 + 13x

Combine like terms: 7x + 13x = 20x
-32 + 20x + 3x2 = 17 + -13x + -17 + 13x

Reorder the terms:
-32 + 20x + 3x2 = 17 + -17 + -13x + 13x

Combine like terms: 17 + -17 = 0
-32 + 20x + 3x2 = 0 + -13x + 13x
-32 + 20x + 3x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-32 + 20x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-8, 1.333333333}

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