2a^2+5a=-4(a+1)

Solution for 2a^2+5a=-4(a+1) equation:

Simplifying
2a2 + 5a = -4(a + 1)

Reorder the terms:
5a + 2a2 = -4(a + 1)

Reorder the terms:
5a + 2a2 = -4(1 + a)
5a + 2a2 = (1 * -4 + a * -4)
5a + 2a2 = (-4 + -4a)

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

Solving for variable 'a'.

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

Combine like terms: 5a + 4a = 9a
4 + 9a + 2a2 = -4 + -4a + 4 + 4a

Reorder the terms:
4 + 9a + 2a2 = -4 + 4 + -4a + 4a

Combine like terms: -4 + 4 = 0
4 + 9a + 2a2 = 0 + -4a + 4a
4 + 9a + 2a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
4 + 9a + 2a2 = 0

Factor a trinomial.
(4 + a)(1 + 2a) = 0

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

Simplifying
4 + a = 0

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

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

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

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

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-4, -0.5}