4a(a-7)-15=0

Solution for 4a(a-7)-15=0 equation:

Simplifying
4a(a + -7) + -15 = 0

Reorder the terms:
4a(-7 + a) + -15 = 0
(-7 * 4a + a * 4a) + -15 = 0
(-28a + 4a2) + -15 = 0

Reorder the terms:
-15 + -28a + 4a2 = 0

Solving
-15 + -28a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -2a)(15 + -2a) = 0

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 '(15 + -2a)' equal to zero and attempt to solve:

Simplifying
15 + -2a = 0

Solving
15 + -2a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2a = 0 + -15
-2a = 0 + -15

Combine like terms: 0 + -15 = -15
-2a = -15

Divide each side by '-2'.
a = 7.5

Simplifying
a = 7.5
Solution
a = {-0.5, 7.5}