6x^2=x(9x+13)-2(x^2-x+8)

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Solution for 6x^2=x(9x+13)-2(x^2-x+8) equation: 


Simplifying
6x2 = x(9x + 13) + -2(x2 + -1x + 8)

Reorder the terms:
6x2 = x(13 + 9x) + -2(x2 + -1x + 8)
6x2 = (13 * x + 9x * x) + -2(x2 + -1x + 8)
6x2 = (13x + 9x2) + -2(x2 + -1x + 8)

Reorder the terms:
6x2 = 13x + 9x2 + -2(8 + -1x + x2)
6x2 = 13x + 9x2 + (8 * -2 + -1x * -2 + x2 * -2)
6x2 = 13x + 9x2 + (-16 + 2x + -2x2)

Reorder the terms:
6x2 = -16 + 13x + 2x + 9x2 + -2x2

Combine like terms: 13x + 2x = 15x
6x2 = -16 + 15x + 9x2 + -2x2

Combine like terms: 9x2 + -2x2 = 7x2
6x2 = -16 + 15x + 7x2

Solving
6x2 = -16 + 15x + 7x2

Solving for variable 'x'.

Reorder the terms:
16 + -15x + 6x2 + -7x2 = -16 + 15x + 7x2 + 16 + -15x + -7x2

Combine like terms: 6x2 + -7x2 = -1x2
16 + -15x + -1x2 = -16 + 15x + 7x2 + 16 + -15x + -7x2

Reorder the terms:
16 + -15x + -1x2 = -16 + 16 + 15x + -15x + 7x2 + -7x2

Combine like terms: -16 + 16 = 0
16 + -15x + -1x2 = 0 + 15x + -15x + 7x2 + -7x2
16 + -15x + -1x2 = 15x + -15x + 7x2 + -7x2

Combine like terms: 15x + -15x = 0
16 + -15x + -1x2 = 0 + 7x2 + -7x2
16 + -15x + -1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
16 + -15x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(16 + x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {1, -16}

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