5x=(4x^2-3x+6)

Solution for 5x=(4x^2-3x+6) equation:

Simplifying
5x = (4x2 + -3x + 6)

Reorder the terms:
5x = (6 + -3x + 4x2)

Remove parenthesis around (6 + -3x + 4x2)
5x = 6 + -3x + 4x2

Solving
5x = 6 + -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + 3x + -4x2 = 6 + -3x + 4x2 + -6 + 3x + -4x2

Combine like terms: 5x + 3x = 8x
-6 + 8x + -4x2 = 6 + -3x + 4x2 + -6 + 3x + -4x2

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

Combine like terms: 6 + -6 = 0
-6 + 8x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2
-6 + 8x + -4x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
-6 + 8x + -4x2 = 0 + 4x2 + -4x2
-6 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 4x + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 4x + -2x2 = 0

Solving
-3 + 4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -2x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2x + x2 = 0 + -1.5
-2x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2x + x2 = -1.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -1.5 + 1

Reorder the terms:
1 + -2x + x2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + -2x + x2 = -0.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -0.5

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.