-2a^2+30a=4a+60

Solution for -2a^2+30a=4a+60 equation:

Simplifying
-2a2 + 30a = 4a + 60

Reorder the terms:
30a + -2a2 = 4a + 60

Reorder the terms:
30a + -2a2 = 60 + 4a

Solving
30a + -2a2 = 60 + 4a

Solving for variable 'a'.

Reorder the terms:
-60 + 30a + -4a + -2a2 = 60 + 4a + -60 + -4a

Combine like terms: 30a + -4a = 26a
-60 + 26a + -2a2 = 60 + 4a + -60 + -4a

Reorder the terms:
-60 + 26a + -2a2 = 60 + -60 + 4a + -4a

Combine like terms: 60 + -60 = 0
-60 + 26a + -2a2 = 0 + 4a + -4a
-60 + 26a + -2a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-60 + 26a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 13a + -1a2) = 0

Factor a trinomial.
2((-10 + a)(3 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + a)' equal to zero and attempt to solve:

Simplifying
-10 + a = 0

Solving
-10 + a = 0

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

Add '10' to each side of the equation.
-10 + 10 + a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + a = 0 + 10
a = 0 + 10

Combine like terms: 0 + 10 = 10
a = 10

Simplifying
a = 10
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {10, 3}