a(a-5)=-6(a-7)

Solution for a(a-5)=-6(a-7) equation:

Simplifying
a(a + -5) = -6(a + -7)

Reorder the terms:
a(-5 + a) = -6(a + -7)
(-5 * a + a * a) = -6(a + -7)
(-5a + a2) = -6(a + -7)

Reorder the terms:
-5a + a2 = -6(-7 + a)
-5a + a2 = (-7 * -6 + a * -6)
-5a + a2 = (42 + -6a)

Solving
-5a + a2 = 42 + -6a

Solving for variable 'a'.

Reorder the terms:
-42 + -5a + 6a + a2 = 42 + -6a + -42 + 6a

Combine like terms: -5a + 6a = 1a
-42 + 1a + a2 = 42 + -6a + -42 + 6a

Reorder the terms:
-42 + 1a + a2 = 42 + -42 + -6a + 6a

Combine like terms: 42 + -42 = 0
-42 + 1a + a2 = 0 + -6a + 6a
-42 + 1a + a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
-42 + 1a + a2 = 0

Factor a trinomial.
(-7 + -1a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-7, 6}