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

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


Simplifying
3a(a + -4) + 7(a + -4) = 0

Reorder the terms:
3a(-4 + a) + 7(a + -4) = 0
(-4 * 3a + a * 3a) + 7(a + -4) = 0
(-12a + 3a2) + 7(a + -4) = 0

Reorder the terms:
-12a + 3a2 + 7(-4 + a) = 0
-12a + 3a2 + (-4 * 7 + a * 7) = 0
-12a + 3a2 + (-28 + 7a) = 0

Reorder the terms:
-28 + -12a + 7a + 3a2 = 0

Combine like terms: -12a + 7a = -5a
-28 + -5a + 3a2 = 0

Solving
-28 + -5a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -3a)(4 + -1a) = 0


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

Simplifying
-7 + -3a = 0

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

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

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

Divide each side by '-3'.
a = -2.333333333

Simplifying
a = -2.333333333

Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2.333333333, 4}

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