(a-4)(a-7)=0

Solution for (a-4)(a-7)=0 equation:

Simplifying
(a + -4)(a + -7) = 0

Reorder the terms:
(-4 + a)(a + -7) = 0

Reorder the terms:
(-4 + a)(-7 + a) = 0

Multiply (-4 + a) * (-7 + a)
(-4(-7 + a) + a(-7 + a)) = 0
((-7 * -4 + a * -4) + a(-7 + a)) = 0
((28 + -4a) + a(-7 + a)) = 0
(28 + -4a + (-7 * a + a * a)) = 0
(28 + -4a + (-7a + a2)) = 0

Combine like terms: -4a + -7a = -11a
(28 + -11a + a2) = 0

Solving
28 + -11a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -1a)(7 + -1a) = 0

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

Simplifying
7 + -1a = 0

Solving
7 + -1a = 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 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {4, 7}