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

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

Simplifying
4a2 + a + -5 = 2a + -2

Reorder the terms:
-5 + a + 4a2 = 2a + -2

Reorder the terms:
-5 + a + 4a2 = -2 + 2a

Solving
-5 + a + 4a2 = -2 + 2a

Solving for variable 'a'.

Reorder the terms:
-5 + 2 + a + -2a + 4a2 = -2 + 2a + 2 + -2a

Combine like terms: -5 + 2 = -3
-3 + a + -2a + 4a2 = -2 + 2a + 2 + -2a

Combine like terms: a + -2a = -1a
-3 + -1a + 4a2 = -2 + 2a + 2 + -2a

Reorder the terms:
-3 + -1a + 4a2 = -2 + 2 + 2a + -2a

Combine like terms: -2 + 2 = 0
-3 + -1a + 4a2 = 0 + 2a + -2a
-3 + -1a + 4a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-3 + -1a + 4a2 = 0

Factor a trinomial.
(-3 + -4a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve:

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 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 + -4a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4a = 0 + 3
-4a = 0 + 3

Combine like terms: 0 + 3 = 3
-4a = 3

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-0.75, 1}