4x^2+6x-17=23-21x

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Solution for 4x^2+6x-17=23-21x equation: 


Simplifying
4x2 + 6x + -17 = 23 + -21x

Reorder the terms:
-17 + 6x + 4x2 = 23 + -21x

Solving
-17 + 6x + 4x2 = 23 + -21x

Solving for variable 'x'.

Reorder the terms:
-17 + -23 + 6x + 21x + 4x2 = 23 + -21x + -23 + 21x

Combine like terms: -17 + -23 = -40
-40 + 6x + 21x + 4x2 = 23 + -21x + -23 + 21x

Combine like terms: 6x + 21x = 27x
-40 + 27x + 4x2 = 23 + -21x + -23 + 21x

Reorder the terms:
-40 + 27x + 4x2 = 23 + -23 + -21x + 21x

Combine like terms: 23 + -23 = 0
-40 + 27x + 4x2 = 0 + -21x + 21x
-40 + 27x + 4x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
-40 + 27x + 4x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -4x) = 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 '(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
Solution
x = {-8, 1.25}

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