3a-42=-3a(a+4)

Solution for 3a-42=-3a(a+4) equation:

Simplifying
3a + -42 = -3a(a + 4)

Reorder the terms:
-42 + 3a = -3a(a + 4)

Reorder the terms:
-42 + 3a = -3a(4 + a)
-42 + 3a = (4 * -3a + a * -3a)
-42 + 3a = (-12a + -3a2)

Solving
-42 + 3a = -12a + -3a2

Solving for variable 'a'.

Combine like terms: 3a + 12a = 15a
-42 + 15a + 3a2 = -12a + -3a2 + 12a + 3a2

Reorder the terms:
-42 + 15a + 3a2 = -12a + 12a + -3a2 + 3a2

Combine like terms: -12a + 12a = 0
-42 + 15a + 3a2 = 0 + -3a2 + 3a2
-42 + 15a + 3a2 = -3a2 + 3a2

Combine like terms: -3a2 + 3a2 = 0
-42 + 15a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5a + a2) = 0

Factor a trinomial.
3((-7 + -1a)(2 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve:

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-7, 2}