(2a+3)(a-1)=7

Solution for (2a+3)(a-1)=7 equation:

Simplifying
(2a + 3)(a + -1) = 7

Reorder the terms:
(3 + 2a)(a + -1) = 7

Reorder the terms:
(3 + 2a)(-1 + a) = 7

Multiply (3 + 2a) * (-1 + a)
(3(-1 + a) + 2a * (-1 + a)) = 7
((-1 * 3 + a * 3) + 2a * (-1 + a)) = 7
((-3 + 3a) + 2a * (-1 + a)) = 7
(-3 + 3a + (-1 * 2a + a * 2a)) = 7
(-3 + 3a + (-2a + 2a2)) = 7

Combine like terms: 3a + -2a = 1a
(-3 + 1a + 2a2) = 7

Solving
-3 + 1a + 2a2 = 7

Solving for variable 'a'.

Reorder the terms:
-3 + -7 + 1a + 2a2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + 1a + 2a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + 1a + 2a2 = 0

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

Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve:

Simplifying
-5 + -2a = 0

Solving
-5 + -2a = 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 + -2a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5

Combine like terms: 0 + 5 = 5
-2a = 5

Divide each side by '-2'.
a = -2.5

Simplifying
a = -2.5
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 = {-2.5, 2}