7=a(a-6)

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

Simplifying
7 = a(a + -6)

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

Solving
7 = -6a + a2

Solving for variable 'a'.

Reorder the terms:
7 + 6a + -1a2 = -6a + 6a + a2 + -1a2

Combine like terms: -6a + 6a = 0
7 + 6a + -1a2 = 0 + a2 + -1a2
7 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
7 + 6a + -1a2 = 0

Factor a trinomial.
(7 + -1a)(1 + a) = 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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
Solution
a = {7, -1}