4(1+2a)=-6a(a-3)

Solution for 4(1+2a)=-6a(a-3) equation:

Simplifying
4(1 + 2a) = -6a(a + -3)
(1 * 4 + 2a * 4) = -6a(a + -3)
(4 + 8a) = -6a(a + -3)

Reorder the terms:
4 + 8a = -6a(-3 + a)
4 + 8a = (-3 * -6a + a * -6a)
4 + 8a = (18a + -6a2)

Solving
4 + 8a = 18a + -6a2

Solving for variable 'a'.

Combine like terms: 8a + -18a = -10a
4 + -10a + 6a2 = 18a + -6a2 + -18a + 6a2

Reorder the terms:
4 + -10a + 6a2 = 18a + -18a + -6a2 + 6a2

Combine like terms: 18a + -18a = 0
4 + -10a + 6a2 = 0 + -6a2 + 6a2
4 + -10a + 6a2 = -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
4 + -10a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5a + 3a2) = 0

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

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

Simplifying
2 + -3a = 0

Solving
2 + -3a = 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 + -3a = 0 + -2

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

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

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
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
Solution
a = {0.6666666667, 1}