5a(5+7a)=7a+5

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

Simplifying
5a(5 + 7a) = 7a + 5
(5 * 5a + 7a * 5a) = 7a + 5
(25a + 35a2) = 7a + 5

Reorder the terms:
25a + 35a2 = 5 + 7a

Solving
25a + 35a2 = 5 + 7a

Solving for variable 'a'.

Reorder the terms:
-5 + 25a + -7a + 35a2 = 5 + 7a + -5 + -7a

Combine like terms: 25a + -7a = 18a
-5 + 18a + 35a2 = 5 + 7a + -5 + -7a

Reorder the terms:
-5 + 18a + 35a2 = 5 + -5 + 7a + -7a

Combine like terms: 5 + -5 = 0
-5 + 18a + 35a2 = 0 + 7a + -7a
-5 + 18a + 35a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-5 + 18a + 35a2 = 0

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

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

Simplifying
-5 + -7a = 0

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

Combine like terms: -5 + 5 = 0
0 + -7a = 0 + 5
-7a = 0 + 5

Combine like terms: 0 + 5 = 5
-7a = 5

Divide each side by '-7'.
a = -0.7142857143

Simplifying
a = -0.7142857143
Subproblem 2
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
Solution
a = {-0.7142857143, 0.2}