4a^2=15a+4

Solution for 4a^2=15a+4 equation:

Simplifying
4a2 = 15a + 4

Reorder the terms:
4a2 = 4 + 15a

Solving
4a2 = 4 + 15a

Solving for variable 'a'.

Reorder the terms:
-4 + -15a + 4a2 = 4 + 15a + -4 + -15a

Reorder the terms:
-4 + -15a + 4a2 = 4 + -4 + 15a + -15a

Combine like terms: 4 + -4 = 0
-4 + -15a + 4a2 = 0 + 15a + -15a
-4 + -15a + 4a2 = 15a + -15a

Combine like terms: 15a + -15a = 0
-4 + -15a + 4a2 = 0

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

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

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-0.25, 4}