6a(5a)-7a+4a=(9)

Solution for 6a(5a)-7a+4a=(9) equation:

Simplifying
6a(5a) + -7a + 4a = (9)

Remove parenthesis around (5a)
6a * 5a + -7a + 4a = (9)

Reorder the terms for easier multiplication:
6 * 5a * a + -7a + 4a = (9)

Multiply 6 * 5
30a * a + -7a + 4a = (9)

Multiply a * a
30a2 + -7a + 4a = (9)

Reorder the terms:
-7a + 4a + 30a2 = (9)

Combine like terms: -7a + 4a = -3a
-3a + 30a2 = (9)
-3a + 30a2 = 9

Solving
-3a + 30a2 = 9

Solving for variable 'a'.

Reorder the terms:
-9 + -3a + 30a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -3a + 30a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1a + 10a2) = 0

Factor a trinomial.
3((-1 + -2a)(3 + -5a)) = 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 '(3 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

Solving
3 + -5a = 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 + -5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5a = 0 + -3
-5a = 0 + -3

Combine like terms: 0 + -3 = -3
-5a = -3

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {-0.5, 0.6}