4x^2-10x-6=x^2+2

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Solution for 4x^2-10x-6=x^2+2 equation: 


Simplifying
4x2 + -10x + -6 = x2 + 2

Reorder the terms:
-6 + -10x + 4x2 = x2 + 2

Reorder the terms:
-6 + -10x + 4x2 = 2 + x2

Solving
-6 + -10x + 4x2 = 2 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -2 + -10x + 4x2 + -1x2 = 2 + x2 + -2 + -1x2

Combine like terms: -6 + -2 = -8
-8 + -10x + 4x2 + -1x2 = 2 + x2 + -2 + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-8 + -10x + 3x2 = 2 + x2 + -2 + -1x2

Reorder the terms:
-8 + -10x + 3x2 = 2 + -2 + x2 + -1x2

Combine like terms: 2 + -2 = 0
-8 + -10x + 3x2 = 0 + x2 + -1x2
-8 + -10x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -10x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.6666666667, 4}

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