3x^2+4x-17=7-10x

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Solution for 3x^2+4x-17=7-10x equation: 


Simplifying
3x2 + 4x + -17 = 7 + -10x

Reorder the terms:
-17 + 4x + 3x2 = 7 + -10x

Solving
-17 + 4x + 3x2 = 7 + -10x

Solving for variable 'x'.

Reorder the terms:
-17 + -7 + 4x + 10x + 3x2 = 7 + -10x + -7 + 10x

Combine like terms: -17 + -7 = -24
-24 + 4x + 10x + 3x2 = 7 + -10x + -7 + 10x

Combine like terms: 4x + 10x = 14x
-24 + 14x + 3x2 = 7 + -10x + -7 + 10x

Reorder the terms:
-24 + 14x + 3x2 = 7 + -7 + -10x + 10x

Combine like terms: 7 + -7 = 0
-24 + 14x + 3x2 = 0 + -10x + 10x
-24 + 14x + 3x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-24 + 14x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -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 '(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 = {-6, 1.333333333}

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