4a^2=-3a+1

Solution for 4a^2=-3a+1 equation:

Simplifying
4a2 = -3a + 1

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

Solving
4a2 = 1 + -3a

Solving for variable 'a'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {-1, 0.25}