6(x^2+3)+8x-2x^2=x^2+8+x+10

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Solution for 6(x^2+3)+8x-2x^2=x^2+8+x+10 equation: 


Simplifying
6(x2 + 3) + 8x + -2x2 = x2 + 8 + x + 10

Reorder the terms:
6(3 + x2) + 8x + -2x2 = x2 + 8 + x + 10
(3 * 6 + x2 * 6) + 8x + -2x2 = x2 + 8 + x + 10
(18 + 6x2) + 8x + -2x2 = x2 + 8 + x + 10

Reorder the terms:
18 + 8x + 6x2 + -2x2 = x2 + 8 + x + 10

Combine like terms: 6x2 + -2x2 = 4x2
18 + 8x + 4x2 = x2 + 8 + x + 10

Reorder the terms:
18 + 8x + 4x2 = 8 + 10 + x + x2

Combine like terms: 8 + 10 = 18
18 + 8x + 4x2 = 18 + x + x2

Add '-18' to each side of the equation.
18 + 8x + -18 + 4x2 = 18 + x + -18 + x2

Reorder the terms:
18 + -18 + 8x + 4x2 = 18 + x + -18 + x2

Combine like terms: 18 + -18 = 0
0 + 8x + 4x2 = 18 + x + -18 + x2
8x + 4x2 = 18 + x + -18 + x2

Reorder the terms:
8x + 4x2 = 18 + -18 + x + x2

Combine like terms: 18 + -18 = 0
8x + 4x2 = 0 + x + x2
8x + 4x2 = x + x2

Solving
8x + 4x2 = x + x2

Solving for variable 'x'.

Reorder the terms:
8x + -1x + 4x2 + -1x2 = x + x2 + -1x + -1x2

Combine like terms: 8x + -1x = 7x
7x + 4x2 + -1x2 = x + x2 + -1x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
7x + 3x2 = x + x2 + -1x + -1x2

Reorder the terms:
7x + 3x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
7x + 3x2 = 0 + x2 + -1x2
7x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 3x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0, -2.333333333}

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