5x^2(2x^2-6x+7)=

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Solution for 5x^2(2x^2-6x+7)= equation: 


Simplifying
5x2(2x2 + -6x + 7) = 0

Reorder the terms:
5x2(7 + -6x + 2x2) = 0
(7 * 5x2 + -6x * 5x2 + 2x2 * 5x2) = 0
(35x2 + -30x3 + 10x4) = 0

Solving
35x2 + -30x3 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(7 + -6x + 2x2) = 0

Ignore the factor 5.

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 '(7 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x + 2x2 = 0

Solving
7 + -6x + 2x2 = 0

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

Divide each side by '2'.
3.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -3x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -3x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -3x + x2 = 0 + -3.5
-3x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-3x + x2 = -3.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -3.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -3.5 + 2.25

Combine like terms: -3.5 + 2.25 = -1.25
2.25 + -3x + x2 = -1.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -1.25

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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