0=(2a-7)(a+3)

Solution for 0=(2a-7)(a+3) equation:

Simplifying
0 = (2a + -7)(a + 3)

Reorder the terms:
0 = (-7 + 2a)(a + 3)

Reorder the terms:
0 = (-7 + 2a)(3 + a)

Multiply (-7 + 2a) * (3 + a)
0 = (-7(3 + a) + 2a * (3 + a))
0 = ((3 * -7 + a * -7) + 2a * (3 + a))
0 = ((-21 + -7a) + 2a * (3 + a))
0 = (-21 + -7a + (3 * 2a + a * 2a))
0 = (-21 + -7a + (6a + 2a2))

Combine like terms: -7a + 6a = -1a
0 = (-21 + -1a + 2a2)

Solving
0 = -21 + -1a + 2a2

Solving for variable 'a'.

Combine like terms: 0 + 21 = 21
21 + a + -2a2 = -21 + -1a + 2a2 + 21 + a + -2a2

Reorder the terms:
21 + a + -2a2 = -21 + 21 + -1a + a + 2a2 + -2a2

Combine like terms: -21 + 21 = 0
21 + a + -2a2 = 0 + -1a + a + 2a2 + -2a2
21 + a + -2a2 = -1a + a + 2a2 + -2a2

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

Combine like terms: 2a2 + -2a2 = 0
21 + a + -2a2 = 0

Factor a trinomial.
(7 + -2a)(3 + a) = 0

Subproblem 1
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

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

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

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

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

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

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

Simplifying
a = -3
Solution
a = {3.5, -3}