-4a^2+3a=10-5a^2

Solution for -4a^2+3a=10-5a^2 equation:

Simplifying
-4a2 + 3a = 10 + -5a2

Reorder the terms:
3a + -4a2 = 10 + -5a2

Solving
3a + -4a2 = 10 + -5a2

Solving for variable 'a'.

Reorder the terms:
-10 + 3a + -4a2 + 5a2 = 10 + -5a2 + -10 + 5a2

Combine like terms: -4a2 + 5a2 = 1a2
-10 + 3a + 1a2 = 10 + -5a2 + -10 + 5a2

Reorder the terms:
-10 + 3a + 1a2 = 10 + -10 + -5a2 + 5a2

Combine like terms: 10 + -10 = 0
-10 + 3a + 1a2 = 0 + -5a2 + 5a2
-10 + 3a + 1a2 = -5a2 + 5a2

Combine like terms: -5a2 + 5a2 = 0
-10 + 3a + 1a2 = 0

Factor a trinomial.
(-5 + -1a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -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 = {-5, 2}