2x^2+3=3x^4-5

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Solution for 2x^2+3=3x^4-5 equation: 


Simplifying
2x2 + 3 = 3x4 + -5

Reorder the terms:
3 + 2x2 = 3x4 + -5

Reorder the terms:
3 + 2x2 = -5 + 3x4

Solving
3 + 2x2 = -5 + 3x4

Solving for variable 'x'.

Reorder the terms:
3 + 5 + 2x2 + -3x4 = -5 + 3x4 + 5 + -3x4

Combine like terms: 3 + 5 = 8
8 + 2x2 + -3x4 = -5 + 3x4 + 5 + -3x4

Reorder the terms:
8 + 2x2 + -3x4 = -5 + 5 + 3x4 + -3x4

Combine like terms: -5 + 5 = 0
8 + 2x2 + -3x4 = 0 + 3x4 + -3x4
8 + 2x2 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
8 + 2x2 + -3x4 = 0

Factor a trinomial.
(2 + -1x2)(4 + 3x2) = 0


Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(4 + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x2 = 0

Solving
4 + 3x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x2 = 0 + -4
3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
3x2 = -4

Divide each side by '3'.
x2 = -1.333333333

Simplifying
x2 = -1.333333333

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.414213562, 1.414213562}

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