3d^2+4d^2=7d^4

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

Simplifying
3d2 + 4d2 = 7d4

Combine like terms: 3d2 + 4d2 = 7d2
7d2 = 7d4

Solving
7d2 = 7d4

Solving for variable 'd'.

Combine like terms: 7d4 + -7d4 = 0
7d2 + -7d4 = 0

Factor out the Greatest Common Factor (GCF), '7d2'.
7d2(1 + -1d2) = 0

Factor a difference between two squares.
7d2((1 + d)(1 + -1d)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'd2' equal to zero and attempt to solve:

Simplifying
d2 = 0

Solving
d2 = 0

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

Simplifying
d2 = 0

Take the square root of each side:
d = {0}
Subproblem 2
Set the factor '(1 + d)' equal to zero and attempt to solve:

Simplifying
1 + d = 0

Solving
1 + d = 0

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

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

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

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

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

Simplifying
1 + -1d = 0

Solving
1 + -1d = 0

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

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

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

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

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

Simplifying
d = 1
Solution
d = {0, -1, 1}