7a(a+5)-(a+5)=0

Solution for 7a(a+5)-(a+5)=0 equation:

Simplifying
7a(a + 5) + -1(a + 5) = 0

Reorder the terms:
7a(5 + a) + -1(a + 5) = 0
(5 * 7a + a * 7a) + -1(a + 5) = 0
(35a + 7a2) + -1(a + 5) = 0

Reorder the terms:
35a + 7a2 + -1(5 + a) = 0
35a + 7a2 + (5 * -1 + a * -1) = 0
35a + 7a2 + (-5 + -1a) = 0

Reorder the terms:
-5 + 35a + -1a + 7a2 = 0

Combine like terms: 35a + -1a = 34a
-5 + 34a + 7a2 = 0

Solving
-5 + 34a + 7a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(1 + -7a) = 0

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

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(1 + -7a)' equal to zero and attempt to solve:

Simplifying
1 + -7a = 0

Solving
1 + -7a = 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 + -7a = 0 + -1

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

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

Divide each side by '-7'.
a = 0.1428571429

Simplifying
a = 0.1428571429
Solution
a = {-5, 0.1428571429}