5a-5=15a^2+4a-7

Solution for 5a-5=15a^2+4a-7 equation:

Simplifying
5a + -5 = 15a2 + 4a + -7

Reorder the terms:
-5 + 5a = 15a2 + 4a + -7

Reorder the terms:
-5 + 5a = -7 + 4a + 15a2

Solving
-5 + 5a = -7 + 4a + 15a2

Solving for variable 'a'.

Reorder the terms:
-5 + 7 + 5a + -4a + -15a2 = -7 + 4a + 15a2 + 7 + -4a + -15a2

Combine like terms: -5 + 7 = 2
2 + 5a + -4a + -15a2 = -7 + 4a + 15a2 + 7 + -4a + -15a2

Combine like terms: 5a + -4a = 1a
2 + 1a + -15a2 = -7 + 4a + 15a2 + 7 + -4a + -15a2

Reorder the terms:
2 + 1a + -15a2 = -7 + 7 + 4a + -4a + 15a2 + -15a2

Combine like terms: -7 + 7 = 0
2 + 1a + -15a2 = 0 + 4a + -4a + 15a2 + -15a2
2 + 1a + -15a2 = 4a + -4a + 15a2 + -15a2

Combine like terms: 4a + -4a = 0
2 + 1a + -15a2 = 0 + 15a2 + -15a2
2 + 1a + -15a2 = 15a2 + -15a2

Combine like terms: 15a2 + -15a2 = 0
2 + 1a + -15a2 = 0

Factor a trinomial.
(2 + -5a)(1 + 3a) = 0

Subproblem 1
Set the factor '(2 + -5a)' equal to zero and attempt to solve:

Simplifying
2 + -5a = 0

Solving
2 + -5a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a = 0 + -2
-5a = 0 + -2

Combine like terms: 0 + -2 = -2
-5a = -2

Divide each side by '-5'.
a = 0.4

Simplifying
a = 0.4
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 = {0.4, -0.3333333333}