15x-x^2+6=-4x^2-2x-4

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Solution for 15x-x^2+6=-4x^2-2x-4 equation: 


Simplifying
15x + -1x2 + 6 = -4x2 + -2x + -4

Reorder the terms:
6 + 15x + -1x2 = -4x2 + -2x + -4

Reorder the terms:
6 + 15x + -1x2 = -4 + -2x + -4x2

Solving
6 + 15x + -1x2 = -4 + -2x + -4x2

Solving for variable 'x'.

Reorder the terms:
6 + 4 + 15x + 2x + -1x2 + 4x2 = -4 + -2x + -4x2 + 4 + 2x + 4x2

Combine like terms: 6 + 4 = 10
10 + 15x + 2x + -1x2 + 4x2 = -4 + -2x + -4x2 + 4 + 2x + 4x2

Combine like terms: 15x + 2x = 17x
10 + 17x + -1x2 + 4x2 = -4 + -2x + -4x2 + 4 + 2x + 4x2

Combine like terms: -1x2 + 4x2 = 3x2
10 + 17x + 3x2 = -4 + -2x + -4x2 + 4 + 2x + 4x2

Reorder the terms:
10 + 17x + 3x2 = -4 + 4 + -2x + 2x + -4x2 + 4x2

Combine like terms: -4 + 4 = 0
10 + 17x + 3x2 = 0 + -2x + 2x + -4x2 + 4x2
10 + 17x + 3x2 = -2x + 2x + -4x2 + 4x2

Combine like terms: -2x + 2x = 0
10 + 17x + 3x2 = 0 + -4x2 + 4x2
10 + 17x + 3x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
10 + 17x + 3x2 = 0

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


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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, -0.6666666667}

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