13a(-45a+27)=13(-8a-10)

Solution for 13a(-45a+27)=13(-8a-10) equation:

Simplifying
13a(-45a + 27) = 13(-8a + -10)

Reorder the terms:
13a(27 + -45a) = 13(-8a + -10)
(27 * 13a + -45a * 13a) = 13(-8a + -10)
(351a + -585a2) = 13(-8a + -10)

Reorder the terms:
351a + -585a2 = 13(-10 + -8a)
351a + -585a2 = (-10 * 13 + -8a * 13)
351a + -585a2 = (-130 + -104a)

Solving
351a + -585a2 = -130 + -104a

Solving for variable 'a'.

Reorder the terms:
130 + 351a + 104a + -585a2 = -130 + -104a + 130 + 104a

Combine like terms: 351a + 104a = 455a
130 + 455a + -585a2 = -130 + -104a + 130 + 104a

Reorder the terms:
130 + 455a + -585a2 = -130 + 130 + -104a + 104a

Combine like terms: -130 + 130 = 0
130 + 455a + -585a2 = 0 + -104a + 104a
130 + 455a + -585a2 = -104a + 104a

Combine like terms: -104a + 104a = 0
130 + 455a + -585a2 = 0

Factor out the Greatest Common Factor (GCF), '65'.
65(2 + 7a + -9a2) = 0

Factor a trinomial.
65((1 + -1a)(2 + 9a)) = 0

Ignore the factor 65.
Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Subproblem 2
Set the factor '(2 + 9a)' equal to zero and attempt to solve:

Simplifying
2 + 9a = 0

Solving
2 + 9a = 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 + 9a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9a = 0 + -2
9a = 0 + -2

Combine like terms: 0 + -2 = -2
9a = -2

Divide each side by '9'.
a = -0.2222222222

Simplifying
a = -0.2222222222
Solution
a = {1, -0.2222222222}