34+10x-x^2=x^2+3x+4

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Solution for 34+10x-x^2=x^2+3x+4 equation: 


Simplifying
34 + 10x + -1x2 = x2 + 3x + 4

Reorder the terms:
34 + 10x + -1x2 = 4 + 3x + x2

Solving
34 + 10x + -1x2 = 4 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
34 + -4 + 10x + -3x + -1x2 + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2

Combine like terms: 34 + -4 = 30
30 + 10x + -3x + -1x2 + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2

Combine like terms: 10x + -3x = 7x
30 + 7x + -1x2 + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
30 + 7x + -2x2 = 4 + 3x + x2 + -4 + -3x + -1x2

Reorder the terms:
30 + 7x + -2x2 = 4 + -4 + 3x + -3x + x2 + -1x2

Combine like terms: 4 + -4 = 0
30 + 7x + -2x2 = 0 + 3x + -3x + x2 + -1x2
30 + 7x + -2x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
30 + 7x + -2x2 = 0 + x2 + -1x2
30 + 7x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + 7x + -2x2 = 0

Factor a trinomial.
(6 + -1x)(5 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {6, -2.5}

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