2x^2-10x-7=5+6x-x^2

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Solution for 2x^2-10x-7=5+6x-x^2 equation: 


Simplifying
2x2 + -10x + -7 = 5 + 6x + -1x2

Reorder the terms:
-7 + -10x + 2x2 = 5 + 6x + -1x2

Solving
-7 + -10x + 2x2 = 5 + 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
-7 + -5 + -10x + -6x + 2x2 + x2 = 5 + 6x + -1x2 + -5 + -6x + x2

Combine like terms: -7 + -5 = -12
-12 + -10x + -6x + 2x2 + x2 = 5 + 6x + -1x2 + -5 + -6x + x2

Combine like terms: -10x + -6x = -16x
-12 + -16x + 2x2 + x2 = 5 + 6x + -1x2 + -5 + -6x + x2

Combine like terms: 2x2 + x2 = 3x2
-12 + -16x + 3x2 = 5 + 6x + -1x2 + -5 + -6x + x2

Reorder the terms:
-12 + -16x + 3x2 = 5 + -5 + 6x + -6x + -1x2 + x2

Combine like terms: 5 + -5 = 0
-12 + -16x + 3x2 = 0 + 6x + -6x + -1x2 + x2
-12 + -16x + 3x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
-12 + -16x + 3x2 = 0 + -1x2 + x2
-12 + -16x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12 + -16x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(6 + -1x) = 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 '(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
Solution
x = {-0.6666666667, 6}

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