a(a-3)+7(a-3)=

Solution for a(a-3)+7(a-3)= equation:

Simplifying
a(a + -3) + 7(a + -3) = 0

Reorder the terms:
a(-3 + a) + 7(a + -3) = 0
(-3 * a + a * a) + 7(a + -3) = 0
(-3a + a2) + 7(a + -3) = 0

Reorder the terms:
-3a + a2 + 7(-3 + a) = 0
-3a + a2 + (-3 * 7 + a * 7) = 0
-3a + a2 + (-21 + 7a) = 0

Reorder the terms:
-21 + -3a + 7a + a2 = 0

Combine like terms: -3a + 7a = 4a
-21 + 4a + a2 = 0

Solving
-21 + 4a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -1a)(3 + -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 '(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 = {-7, 3}