(1-4a)(1-7a)=

Solution for (1-4a)(1-7a)= equation:

Simplifying
(1 + -4a)(1 + -7a) = 0

Multiply (1 + -4a) * (1 + -7a)
(1(1 + -7a) + -4a * (1 + -7a)) = 0
((1 * 1 + -7a * 1) + -4a * (1 + -7a)) = 0
((1 + -7a) + -4a * (1 + -7a)) = 0
(1 + -7a + (1 * -4a + -7a * -4a)) = 0
(1 + -7a + (-4a + 28a2)) = 0

Combine like terms: -7a + -4a = -11a
(1 + -11a + 28a2) = 0

Solving
1 + -11a + 28a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -7a = 0

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

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

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

Divide each side by '-7'.
a = 0.1428571429

Simplifying
a = 0.1428571429
Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {0.1428571429, 0.25}