4a^2-10a=6

Solution for 4a^2-10a=6 equation:

Simplifying
4a2 + -10a = 6

Reorder the terms:
-10a + 4a2 = 6

Solving
-10a + 4a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + -10a + 4a2 = 6 + -6

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5a + 2a2) = 0

Factor a trinomial.
2((-1 + -2a)(3 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve:

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

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

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

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.5, 3}