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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -17 + -4 = -21
-21 + 7x + -3x + x2 = 4 + 3x + -4 + -3x

Combine like terms: 7x + -3x = 4x
-21 + 4x + x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-21 + 4x + x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-21 + 4x + x2 = 0 + 3x + -3x
-21 + 4x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}

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