7a^2-38a=-15

Solution for 7a^2-38a=-15 equation:

Simplifying
7a2 + -38a = -15

Reorder the terms:
-38a + 7a2 = -15

Solving
-38a + 7a2 = -15

Solving for variable 'a'.

Reorder the terms:
15 + -38a + 7a2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -38a + 7a2 = 0

Factor a trinomial.
(3 + -7a)(5 + -1a) = 0

Subproblem 1
Set the factor '(3 + -7a)' equal to zero and attempt to solve:

Simplifying
3 + -7a = 0

Solving
3 + -7a = 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 + -7a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7a = 0 + -3
-7a = 0 + -3

Combine like terms: 0 + -3 = -3
-7a = -3

Divide each side by '-7'.
a = 0.4285714286

Simplifying
a = 0.4285714286
Subproblem 2
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
Solution
a = {0.4285714286, 5}