22x^2+23x+11=3+x^2-3x

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Solution for 22x^2+23x+11=3+x^2-3x equation: 


Simplifying
22x2 + 23x + 11 = 3 + x2 + -3x

Reorder the terms:
11 + 23x + 22x2 = 3 + x2 + -3x

Reorder the terms:
11 + 23x + 22x2 = 3 + -3x + x2

Solving
11 + 23x + 22x2 = 3 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
11 + -3 + 23x + 3x + 22x2 + -1x2 = 3 + -3x + x2 + -3 + 3x + -1x2

Combine like terms: 11 + -3 = 8
8 + 23x + 3x + 22x2 + -1x2 = 3 + -3x + x2 + -3 + 3x + -1x2

Combine like terms: 23x + 3x = 26x
8 + 26x + 22x2 + -1x2 = 3 + -3x + x2 + -3 + 3x + -1x2

Combine like terms: 22x2 + -1x2 = 21x2
8 + 26x + 21x2 = 3 + -3x + x2 + -3 + 3x + -1x2

Reorder the terms:
8 + 26x + 21x2 = 3 + -3 + -3x + 3x + x2 + -1x2

Combine like terms: 3 + -3 = 0
8 + 26x + 21x2 = 0 + -3x + 3x + x2 + -1x2
8 + 26x + 21x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
8 + 26x + 21x2 = 0 + x2 + -1x2
8 + 26x + 21x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 26x + 21x2 = 0

Factor a trinomial.
(2 + 3x)(4 + 7x) = 0


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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 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 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {-0.6666666667, -0.5714285714}

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