a(4a-7)-2=0

Solution for a(4a-7)-2=0 equation:

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

Reorder the terms:
a(-7 + 4a) + -2 = 0
(-7 * a + 4a * a) + -2 = 0
(-7a + 4a2) + -2 = 0

Reorder the terms:
-2 + -7a + 4a2 = 0

Solving
-2 + -7a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -4a)(2 + -1a) = 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 '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-0.25, 2}