28a^2-200a+145=-8a+1

Solution for 28a^2-200a+145=-8a+1 equation:

Simplifying
28a2 + -200a + 145 = -8a + 1

Reorder the terms:
145 + -200a + 28a2 = -8a + 1

Reorder the terms:
145 + -200a + 28a2 = 1 + -8a

Solving
145 + -200a + 28a2 = 1 + -8a

Solving for variable 'a'.

Reorder the terms:
145 + -1 + -200a + 8a + 28a2 = 1 + -8a + -1 + 8a

Combine like terms: 145 + -1 = 144
144 + -200a + 8a + 28a2 = 1 + -8a + -1 + 8a

Combine like terms: -200a + 8a = -192a
144 + -192a + 28a2 = 1 + -8a + -1 + 8a

Reorder the terms:
144 + -192a + 28a2 = 1 + -1 + -8a + 8a

Combine like terms: 1 + -1 = 0
144 + -192a + 28a2 = 0 + -8a + 8a
144 + -192a + 28a2 = -8a + 8a

Combine like terms: -8a + 8a = 0
144 + -192a + 28a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + -48a + 7a2) = 0

Factor a trinomial.
4((6 + -7a)(6 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -7a)' equal to zero and attempt to solve:

Simplifying
6 + -7a = 0

Solving
6 + -7a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7a = 0 + -6
-7a = 0 + -6

Combine like terms: 0 + -6 = -6
-7a = -6

Divide each side by '-7'.
a = 0.8571428571

Simplifying
a = 0.8571428571
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {0.8571428571, 6}