6(x^2+1)+4x=3x+8

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Solution for 6(x^2+1)+4x=3x+8 equation: 


Simplifying
6(x2 + 1) + 4x = 3x + 8

Reorder the terms:
6(1 + x2) + 4x = 3x + 8
(1 * 6 + x2 * 6) + 4x = 3x + 8
(6 + 6x2) + 4x = 3x + 8

Reorder the terms:
6 + 4x + 6x2 = 3x + 8

Reorder the terms:
6 + 4x + 6x2 = 8 + 3x

Solving
6 + 4x + 6x2 = 8 + 3x

Solving for variable 'x'.

Reorder the terms:
6 + -8 + 4x + -3x + 6x2 = 8 + 3x + -8 + -3x

Combine like terms: 6 + -8 = -2
-2 + 4x + -3x + 6x2 = 8 + 3x + -8 + -3x

Combine like terms: 4x + -3x = 1x
-2 + 1x + 6x2 = 8 + 3x + -8 + -3x

Reorder the terms:
-2 + 1x + 6x2 = 8 + -8 + 3x + -3x

Combine like terms: 8 + -8 = 0
-2 + 1x + 6x2 = 0 + 3x + -3x
-2 + 1x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-2 + 1x + 6x2 = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.6666666667, 0.5}

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