Simplifying
6x4 + 8x2 = 26x3
Reorder the terms:
8x2 + 6x4 = 26x3
Solving
8x2 + 6x4 = 26x3
Solving for variable 'x'.
Reorder the terms:
8x2 + -26x3 + 6x4 = 26x3 + -26x3
Combine like terms: 26x3 + -26x3 = 0
8x2 + -26x3 + 6x4 = 0
Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(4 + -13x + 3x2) = 0
Factor a trinomial.
2x2((1 + -3x)(4 + -1x)) = 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 '(1 + -3x)' equal to zero and attempt to solve:
Simplifying
1 + -3x = 0
Solving
1 + -3x = 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 + -3x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1
Combine like terms: 0 + -1 = -1
-3x = -1
Divide each side by '-3'.
x = 0.3333333333
Simplifying
x = 0.3333333333
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:
Simplifying
4 + -1x = 0
Solving
4 + -1x = 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 + -1x = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4
Combine like terms: 0 + -4 = -4
-1x = -4
Divide each side by '-1'.
x = 4
Simplifying
x = 4
Solution
x = {0, 0.3333333333, 4}