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

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

Simplifying
(4a + 2)(a + -3) = 0

Reorder the terms:
(2 + 4a)(a + -3) = 0

Reorder the terms:
(2 + 4a)(-3 + a) = 0

Multiply (2 + 4a) * (-3 + a)
(2(-3 + a) + 4a * (-3 + a)) = 0
((-3 * 2 + a * 2) + 4a * (-3 + a)) = 0
((-6 + 2a) + 4a * (-3 + a)) = 0
(-6 + 2a + (-3 * 4a + a * 4a)) = 0
(-6 + 2a + (-12a + 4a2)) = 0

Combine like terms: 2a + -12a = -10a
(-6 + -10a + 4a2) = 0

Solving
-6 + -10a + 4a2 = 0

Solving for variable 'a'.

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

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

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.5, 3}