15a^2-3a=3-7a

Solution for 15a^2-3a=3-7a equation:

Simplifying
15a2 + -3a = 3 + -7a

Reorder the terms:
-3a + 15a2 = 3 + -7a

Solving
-3a + 15a2 = 3 + -7a

Solving for variable 'a'.

Reorder the terms:
-3 + -3a + 7a + 15a2 = 3 + -7a + -3 + 7a

Combine like terms: -3a + 7a = 4a
-3 + 4a + 15a2 = 3 + -7a + -3 + 7a

Reorder the terms:
-3 + 4a + 15a2 = 3 + -3 + -7a + 7a

Combine like terms: 3 + -3 = 0
-3 + 4a + 15a2 = 0 + -7a + 7a
-3 + 4a + 15a2 = -7a + 7a

Combine like terms: -7a + 7a = 0
-3 + 4a + 15a2 = 0

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

Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 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 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 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 + -3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3a = 0 + -1
-3a = 0 + -1

Combine like terms: 0 + -1 = -1
-3a = -1

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {-0.6, 0.3333333333}