8r^2(4r^2-5r+7)=

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Solution for 8r^2(4r^2-5r+7)= equation: 


Simplifying
8r2(4r2 + -5r + 7) = 0

Reorder the terms:
8r2(7 + -5r + 4r2) = 0
(7 * 8r2 + -5r * 8r2 + 4r2 * 8r2) = 0
(56r2 + -40r3 + 32r4) = 0

Solving
56r2 + -40r3 + 32r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8r2'.
8r2(7 + -5r + 4r2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

Move all terms containing r to the left, all other terms to the right.

Simplifying
r2 = 0

Take the square root of each side:
r = {0}

Subproblem 2
Set the factor '(7 + -5r + 4r2)' equal to zero and attempt to solve:

Simplifying
7 + -5r + 4r2 = 0

Solving
7 + -5r + 4r2 = 0

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

Divide each side by '4'.
1.75 + -1.25r + r2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -1.25r + -1.75 + r2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -1.25r + r2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -1.25r + r2 = 0 + -1.75
-1.25r + r2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-1.25r + r2 = -1.75

The r term is -1.25r.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25r + 0.390625 + r2 = -1.75 + 0.390625

Reorder the terms:
0.390625 + -1.25r + r2 = -1.75 + 0.390625

Combine like terms: -1.75 + 0.390625 = -1.359375
0.390625 + -1.25r + r2 = -1.359375

Factor a perfect square on the left side:
(r + -0.625)(r + -0.625) = -1.359375

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.
Solution
r = {0}

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