4x^4+3=7x^2

Solution for 4x^4+3=7x^2 equation:

Simplifying
4x4 + 3 = 7x2

Reorder the terms:
3 + 4x4 = 7x2

Solving
3 + 4x4 = 7x2

Solving for variable 'x'.

Reorder the terms:
3 + -7x2 + 4x4 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
3 + -7x2 + 4x4 = 0

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

Factor a difference between two squares.
(3 + -4x2)((1 + x)(1 + -1x)) = 0

Subproblem 1
Set the factor '(3 + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x2 = 0

Solving
3 + -4x2 = 0

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

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

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

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

Divide each side by '-4'.
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.866025404, 0.866025404, -1, 1}