=a(5a-2)-6(2-5a)

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

Simplifying
0 = a(5a + -2) + -6(2 + -5a)

Reorder the terms:
0 = a(-2 + 5a) + -6(2 + -5a)
0 = (-2 * a + 5a * a) + -6(2 + -5a)
0 = (-2a + 5a2) + -6(2 + -5a)
0 = -2a + 5a2 + (2 * -6 + -5a * -6)
0 = -2a + 5a2 + (-12 + 30a)

Reorder the terms:
0 = -12 + -2a + 30a + 5a2

Combine like terms: -2a + 30a = 28a
0 = -12 + 28a + 5a2

Solving
0 = -12 + 28a + 5a2

Solving for variable 'a'.

Combine like terms: 0 + 12 = 12
12 + -28a + -5a2 = -12 + 28a + 5a2 + 12 + -28a + -5a2

Reorder the terms:
12 + -28a + -5a2 = -12 + 12 + 28a + -28a + 5a2 + -5a2

Combine like terms: -12 + 12 = 0
12 + -28a + -5a2 = 0 + 28a + -28a + 5a2 + -5a2
12 + -28a + -5a2 = 28a + -28a + 5a2 + -5a2

Combine like terms: 28a + -28a = 0
12 + -28a + -5a2 = 0 + 5a2 + -5a2
12 + -28a + -5a2 = 5a2 + -5a2

Combine like terms: 5a2 + -5a2 = 0
12 + -28a + -5a2 = 0

Factor a trinomial.
(2 + -5a)(6 + a) = 0

Subproblem 1
Set the factor '(2 + -5a)' equal to zero and attempt to solve:

Simplifying
2 + -5a = 0

Solving
2 + -5a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a = 0 + -2
-5a = 0 + -2

Combine like terms: 0 + -2 = -2
-5a = -2

Divide each side by '-5'.
a = 0.4

Simplifying
a = 0.4
Subproblem 2
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {0.4, -6}