2a^3-7a+6a=0

Solution for 2a^3-7a+6a=0 equation:

Simplifying
2a3 + -7a + 6a = 0

Reorder the terms:
-7a + 6a + 2a3 = 0

Combine like terms: -7a + 6a = -1a
-1a + 2a3 = 0

Solving
-1a + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + 2a2) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-1 + 2a2)' equal to zero and attempt to solve:

Simplifying
-1 + 2a2 = 0

Solving
-1 + 2a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2a2 = 0 + 1
2a2 = 0 + 1

Combine like terms: 0 + 1 = 1
2a2 = 1

Divide each side by '2'.
a2 = 0.5

Simplifying
a2 = 0.5

Take the square root of each side:
a = {-0.707106781, 0.707106781}
Solution
a = {0, -0.707106781, 0.707106781}