5(r-3)=10r^2-3

Solution for 5(r-3)=10r^2-3 equation:

Simplifying
5(r + -3) = 10r2 + -3

Reorder the terms:
5(-3 + r) = 10r2 + -3
(-3 * 5 + r * 5) = 10r2 + -3
(-15 + 5r) = 10r2 + -3

Reorder the terms:
-15 + 5r = -3 + 10r2

Solving
-15 + 5r = -3 + 10r2

Solving for variable 'r'.

Reorder the terms:
-15 + 3 + 5r + -10r2 = -3 + 10r2 + 3 + -10r2

Combine like terms: -15 + 3 = -12
-12 + 5r + -10r2 = -3 + 10r2 + 3 + -10r2

Reorder the terms:
-12 + 5r + -10r2 = -3 + 3 + 10r2 + -10r2

Combine like terms: -3 + 3 = 0
-12 + 5r + -10r2 = 0 + 10r2 + -10r2
-12 + 5r + -10r2 = 10r2 + -10r2

Combine like terms: 10r2 + -10r2 = 0
-12 + 5r + -10r2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
1.2 + -0.5r + r2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.5r + -1.2 + r2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.5r + r2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.5r + r2 = 0 + -1.2
-0.5r + r2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.5r + r2 = -1.2

The r term is -0.5r.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5r + 0.0625 + r2 = -1.2 + 0.0625

Reorder the terms:
0.0625 + -0.5r + r2 = -1.2 + 0.0625

Combine like terms: -1.2 + 0.0625 = -1.1375
0.0625 + -0.5r + r2 = -1.1375

Factor a perfect square on the left side:
(r + -0.25)(r + -0.25) = -1.1375

Can't calculate square root of the right side.

The solution to this equation could not be determined.