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

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


Simplifying
3x2(2x2 + -3x + 5) = 0

Reorder the terms:
3x2(5 + -3x + 2x2) = 0
(5 * 3x2 + -3x * 3x2 + 2x2 * 3x2) = 0
(15x2 + -9x3 + 6x4) = 0

Solving
15x2 + -9x3 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(5 + -3x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

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

Subproblem 2
Set the factor '(5 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + -3x + 2x2 = 0

Solving
5 + -3x + 2x2 = 0

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

Divide each side by '2'.
2.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1.5x + x2 = 0 + -2.5
-1.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1.5x + x2 = -2.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -2.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -2.5 + 0.5625

Combine like terms: -2.5 + 0.5625 = -1.9375
0.5625 + -1.5x + x2 = -1.9375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -1.9375

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
x = {0}

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