(4a-1)(2a-7)=

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Solution for (4a-1)(2a-7)= equation: 


Simplifying
(4a + -1)(2a + -7) = 0

Reorder the terms:
(-1 + 4a)(2a + -7) = 0

Reorder the terms:
(-1 + 4a)(-7 + 2a) = 0

Multiply (-1 + 4a) * (-7 + 2a)
(-1(-7 + 2a) + 4a * (-7 + 2a)) = 0
((-7 * -1 + 2a * -1) + 4a * (-7 + 2a)) = 0
((7 + -2a) + 4a * (-7 + 2a)) = 0
(7 + -2a + (-7 * 4a + 2a * 4a)) = 0
(7 + -2a + (-28a + 8a2)) = 0

Combine like terms: -2a + -28a = -30a
(7 + -30a + 8a2) = 0

Solving
7 + -30a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -4a)(7 + -2a) = 0


Subproblem 1
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

Subproblem 2
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
Solution
a = {0.25, 3.5}

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