4Z^2+14Z=10Z-3

Solution for 4Z^2+14Z=10Z-3 equation:

Simplifying
4Z2 + 14Z = 10Z + -3

Reorder the terms:
14Z + 4Z2 = 10Z + -3

Reorder the terms:
14Z + 4Z2 = -3 + 10Z

Solving
14Z + 4Z2 = -3 + 10Z

Solving for variable 'Z'.

Reorder the terms:
3 + 14Z + -10Z + 4Z2 = -3 + 10Z + 3 + -10Z

Combine like terms: 14Z + -10Z = 4Z
3 + 4Z + 4Z2 = -3 + 10Z + 3 + -10Z

Reorder the terms:
3 + 4Z + 4Z2 = -3 + 3 + 10Z + -10Z

Combine like terms: -3 + 3 = 0
3 + 4Z + 4Z2 = 0 + 10Z + -10Z
3 + 4Z + 4Z2 = 10Z + -10Z

Combine like terms: 10Z + -10Z = 0
3 + 4Z + 4Z2 = 0

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

Divide each side by '4'.
0.75 + Z + Z2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + Z + -0.75 + Z2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + Z + Z2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + Z + Z2 = 0 + -0.75
Z + Z2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
Z + Z2 = -0.75

The Z term is Z.  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.
 + 0.25 + Z2 = -0.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + Z2 = -0.75 + 0.25

Combine like terms: -0.75 + 0.25 = -0.5
1.25 + Z2 = -0.5

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.