a(2a-7)=15

Solution for a(2a-7)=15 equation:

Simplifying
a(2a + -7) = 15

Reorder the terms:
a(-7 + 2a) = 15
(-7 * a + 2a * a) = 15
(-7a + 2a2) = 15

Solving
-7a + 2a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -7a + 2a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -7a + 2a2 = 0

Factor a trinomial.
(-3 + -2a)(5 + -1a) = 0

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

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-1.5, 5}