10a^2-3a-7=0

Solution for 10a^2-3a-7=0 equation:

Simplifying
10a2 + -3a + -7 = 0

Reorder the terms:
-7 + -3a + 10a2 = 0

Solving
-7 + -3a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -10a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -10a)' equal to zero and attempt to solve:

Simplifying
-7 + -10a = 0

Solving
-7 + -10a = 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 + -10a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10a = 0 + 7
-10a = 0 + 7

Combine like terms: 0 + 7 = 7
-10a = 7

Divide each side by '-10'.
a = -0.7

Simplifying
a = -0.7
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-0.7, 1}