2a^2-3a=4(a+1)

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

Simplifying
2a2 + -3a = 4(a + 1)

Reorder the terms:
-3a + 2a2 = 4(a + 1)

Reorder the terms:
-3a + 2a2 = 4(1 + a)
-3a + 2a2 = (1 * 4 + a * 4)
-3a + 2a2 = (4 + 4a)

Solving
-3a + 2a2 = 4 + 4a

Solving for variable 'a'.

Reorder the terms:
-4 + -3a + -4a + 2a2 = 4 + 4a + -4 + -4a

Combine like terms: -3a + -4a = -7a
-4 + -7a + 2a2 = 4 + 4a + -4 + -4a

Reorder the terms:
-4 + -7a + 2a2 = 4 + -4 + 4a + -4a

Combine like terms: 4 + -4 = 0
-4 + -7a + 2a2 = 0 + 4a + -4a
-4 + -7a + 2a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
-4 + -7a + 2a2 = 0

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

Subproblem 1
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
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 = {-0.5, 4}