(6a-3)(7a-4)=

Solution for (6a-3)(7a-4)= equation:

Simplifying
(6a + -3)(7a + -4) = 0

Reorder the terms:
(-3 + 6a)(7a + -4) = 0

Reorder the terms:
(-3 + 6a)(-4 + 7a) = 0

Multiply (-3 + 6a) * (-4 + 7a)
(-3(-4 + 7a) + 6a * (-4 + 7a)) = 0
((-4 * -3 + 7a * -3) + 6a * (-4 + 7a)) = 0
((12 + -21a) + 6a * (-4 + 7a)) = 0
(12 + -21a + (-4 * 6a + 7a * 6a)) = 0
(12 + -21a + (-24a + 42a2)) = 0

Combine like terms: -21a + -24a = -45a
(12 + -45a + 42a2) = 0

Solving
12 + -45a + 42a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -15a + 14a2) = 0

Factor a trinomial.
3((1 + -2a)(4 + -7a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

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

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

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

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Subproblem 2
Set the factor '(4 + -7a)' equal to zero and attempt to solve:

Simplifying
4 + -7a = 0

Solving
4 + -7a = 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 + -7a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7a = 0 + -4
-7a = 0 + -4

Combine like terms: 0 + -4 = -4
-7a = -4

Divide each side by '-7'.
a = 0.5714285714

Simplifying
a = 0.5714285714
Solution
a = {0.5, 0.5714285714}