14a^2+20a-100=-a-2

Solution for 14a^2+20a-100=-a-2 equation:

Simplifying
14a2 + 20a + -100 = -1a + -2

Reorder the terms:
-100 + 20a + 14a2 = -1a + -2

Reorder the terms:
-100 + 20a + 14a2 = -2 + -1a

Solving
-100 + 20a + 14a2 = -2 + -1a

Solving for variable 'a'.

Reorder the terms:
-100 + 2 + 20a + a + 14a2 = -2 + -1a + 2 + a

Combine like terms: -100 + 2 = -98
-98 + 20a + a + 14a2 = -2 + -1a + 2 + a

Combine like terms: 20a + a = 21a
-98 + 21a + 14a2 = -2 + -1a + 2 + a

Reorder the terms:
-98 + 21a + 14a2 = -2 + 2 + -1a + a

Combine like terms: -2 + 2 = 0
-98 + 21a + 14a2 = 0 + -1a + a
-98 + 21a + 14a2 = -1a + a

Combine like terms: -1a + a = 0
-98 + 21a + 14a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-14 + 3a + 2a2) = 0

Factor a trinomial.
7((-7 + -2a)(2 + -1a)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve:

Simplifying
-7 + -2a = 0

Solving
-7 + -2a = 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 + -2a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2a = 0 + 7
-2a = 0 + 7

Combine like terms: 0 + 7 = 7
-2a = 7

Divide each side by '-2'.
a = -3.5

Simplifying
a = -3.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-3.5, 2}