x^2+5x+5=4x^2+6x-5

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Solution for x^2+5x+5=4x^2+6x-5 equation: 


Simplifying
x2 + 5x + 5 = 4x2 + 6x + -5

Reorder the terms:
5 + 5x + x2 = 4x2 + 6x + -5

Reorder the terms:
5 + 5x + x2 = -5 + 6x + 4x2

Solving
5 + 5x + x2 = -5 + 6x + 4x2

Solving for variable 'x'.

Reorder the terms:
5 + 5 + 5x + -6x + x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: 5 + 5 = 10
10 + 5x + -6x + x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: 5x + -6x = -1x
10 + -1x + x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: x2 + -4x2 = -3x2
10 + -1x + -3x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Reorder the terms:
10 + -1x + -3x2 = -5 + 5 + 6x + -6x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
10 + -1x + -3x2 = 0 + 6x + -6x + 4x2 + -4x2
10 + -1x + -3x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
10 + -1x + -3x2 = 0 + 4x2 + -4x2
10 + -1x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + -1x + -3x2 = 0

Factor a trinomial.
(5 + -3x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {1.666666667, -2}

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