=6a-2a(5-2a)+3a^2

Solution for =6a-2a(5-2a)+3a^2 equation:

Simplifying
0 = 6a + -2a(5 + -2a) + 3a2
0 = 6a + (5 * -2a + -2a * -2a) + 3a2
0 = 6a + (-10a + 4a2) + 3a2

Combine like terms: 6a + -10a = -4a
0 = -4a + 4a2 + 3a2

Combine like terms: 4a2 + 3a2 = 7a2
0 = -4a + 7a2

Solving
0 = -4a + 7a2

Solving for variable 'a'.
Remove the zero:
4a + -7a2 = -4a + 7a2 + 4a + -7a2

Reorder the terms:
4a + -7a2 = -4a + 4a + 7a2 + -7a2

Combine like terms: -4a + 4a = 0
4a + -7a2 = 0 + 7a2 + -7a2
4a + -7a2 = 7a2 + -7a2

Combine like terms: 7a2 + -7a2 = 0
4a + -7a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + -7a) = 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 '(4 + -7a)' equal to zero and attempt to solve:

Simplifying
4 + -7a = 0

Solving
4 + -7a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7a = 0 + -4
-7a = 0 + -4

Combine like terms: 0 + -4 = -4
-7a = -4

Divide each side by '-7'.
a = 0.5714285714

Simplifying
a = 0.5714285714
Solution
a = {0, 0.5714285714}