7x^4-56x^2-7x=3x+5(-2x+x^4)

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Solution for 7x^4-56x^2-7x=3x+5(-2x+x^4) equation: 


Simplifying
7x4 + -56x2 + -7x = 3x + 5(-2x + x4)

Reorder the terms:
-7x + -56x2 + 7x4 = 3x + 5(-2x + x4)
-7x + -56x2 + 7x4 = 3x + (-2x * 5 + x4 * 5)
-7x + -56x2 + 7x4 = 3x + (-10x + 5x4)

Combine like terms: 3x + -10x = -7x
-7x + -56x2 + 7x4 = -7x + 5x4

Add '7x' to each side of the equation.
-7x + -56x2 + 7x + 7x4 = -7x + 7x + 5x4

Reorder the terms:
-7x + 7x + -56x2 + 7x4 = -7x + 7x + 5x4

Combine like terms: -7x + 7x = 0
0 + -56x2 + 7x4 = -7x + 7x + 5x4
-56x2 + 7x4 = -7x + 7x + 5x4

Combine like terms: -7x + 7x = 0
-56x2 + 7x4 = 0 + 5x4
-56x2 + 7x4 = 5x4

Solving
-56x2 + 7x4 = 5x4

Solving for variable 'x'.

Combine like terms: 7x4 + -5x4 = 2x4
-56x2 + 2x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
-56x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-28 + x2) = 0

Ignore the factor 2.

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 '(-28 + x2)' equal to zero and attempt to solve:

Simplifying
-28 + x2 = 0

Solving
-28 + x2 = 0

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

Add '28' to each side of the equation.
-28 + 28 + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + x2 = 0 + 28
x2 = 0 + 28

Combine like terms: 0 + 28 = 28
x2 = 28

Simplifying
x2 = 28

Take the square root of each side:
x = {-5.291502622, 5.291502622}
Solution
x = {0, -5.291502622, 5.291502622}

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