a(4a+3)=7a^3

Solution for a(4a+3)=7a^3 equation:

Simplifying
a(4a + 3) = 7a3

Reorder the terms:
a(3 + 4a) = 7a3
(3 * a + 4a * a) = 7a3
(3a + 4a2) = 7a3

Solving
3a + 4a2 = 7a3

Solving for variable 'a'.

Combine like terms: 7a3 + -7a3 = 0
3a + 4a2 + -7a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(3 + 4a + -7a2) = 0

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

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Subproblem 3
Set the factor '(3 + 7a)' equal to zero and attempt to solve:

Simplifying
3 + 7a = 0

Solving
3 + 7a = 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 + 7a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7a = 0 + -3
7a = 0 + -3

Combine like terms: 0 + -3 = -3
7a = -3

Divide each side by '7'.
a = -0.4285714286

Simplifying
a = -0.4285714286
Solution
a = {0, 1, -0.4285714286}