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

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

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

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

Solving
2x = -3 + 5x + -3x2

Solving for variable 'x'.

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

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

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

Combine like terms: -3 + 3 = 0
3 + -3x + 3x2 = 0 + 5x + -5x + -3x2 + 3x2
3 + -3x + 3x2 = 5x + -5x + -3x2 + 3x2

Combine like terms: 5x + -5x = 0
3 + -3x + 3x2 = 0 + -3x2 + 3x2
3 + -3x + 3x2 = -3x2 + 3x2

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

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

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

Simplifying
1 + -1x + x2 = 0

Solving
1 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1x + x2 = 0 + -1

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

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

The x term is -1x.  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.
-1x + 0.25 + x2 = -1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1x + x2 = -0.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.75

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.