5a^2-28a+3=-7-a

Solution for 5a^2-28a+3=-7-a equation:

Simplifying
5a2 + -28a + 3 = -7 + -1a

Reorder the terms:
3 + -28a + 5a2 = -7 + -1a

Solving
3 + -28a + 5a2 = -7 + -1a

Solving for variable 'a'.

Reorder the terms:
3 + 7 + -28a + a + 5a2 = -7 + -1a + 7 + a

Combine like terms: 3 + 7 = 10
10 + -28a + a + 5a2 = -7 + -1a + 7 + a

Combine like terms: -28a + a = -27a
10 + -27a + 5a2 = -7 + -1a + 7 + a

Reorder the terms:
10 + -27a + 5a2 = -7 + 7 + -1a + a

Combine like terms: -7 + 7 = 0
10 + -27a + 5a2 = 0 + -1a + a
10 + -27a + 5a2 = -1a + a

Combine like terms: -1a + a = 0
10 + -27a + 5a2 = 0

Factor a trinomial.
(2 + -5a)(5 + -1a) = 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 '(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 = {0.4, 5}