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

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

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

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

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

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

Solving
-7 + -34a + 5a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + -5a = 0

Solving
-1 + -5a = 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 + -5a = 0 + 1

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

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

Divide each side by '-5'.
a = -0.2

Simplifying
a = -0.2
Subproblem 2
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
Solution
a = {-0.2, 7}