2x+3(-x^2-1)=5x-2x+4

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Solution for 2x+3(-x^2-1)=5x-2x+4 equation: 


Simplifying
2x + 3(-1x2 + -1) = 5x + -2x + 4

Reorder the terms:
2x + 3(-1 + -1x2) = 5x + -2x + 4
2x + (-1 * 3 + -1x2 * 3) = 5x + -2x + 4
2x + (-3 + -3x2) = 5x + -2x + 4

Reorder the terms:
-3 + 2x + -3x2 = 5x + -2x + 4

Reorder the terms:
-3 + 2x + -3x2 = 4 + 5x + -2x

Combine like terms: 5x + -2x = 3x
-3 + 2x + -3x2 = 4 + 3x

Solving
-3 + 2x + -3x2 = 4 + 3x

Solving for variable 'x'.

Reorder the terms:
-3 + -4 + 2x + -3x + -3x2 = 4 + 3x + -4 + -3x

Combine like terms: -3 + -4 = -7
-7 + 2x + -3x + -3x2 = 4 + 3x + -4 + -3x

Combine like terms: 2x + -3x = -1x
-7 + -1x + -3x2 = 4 + 3x + -4 + -3x

Reorder the terms:
-7 + -1x + -3x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
-7 + -1x + -3x2 = 0 + 3x + -3x
-7 + -1x + -3x2 = 3x + -3x

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + x + 3x2 = 0

Solving
7 + x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.333333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 0.3333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 0.3333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + -2.333333333
0.3333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
0.3333333333x + x2 = -2.333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = -2.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -2.333333333 + 0.25

Combine like terms: -2.333333333 + 0.25 = -2.083333333
0.25 + 0.3333333333x + x2 = -2.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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