4(a-5)(a+7)=

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Solution for 4(a-5)(a+7)= equation: 


Simplifying
4(a + -5)(a + 7) = 0

Reorder the terms:
4(-5 + a)(a + 7) = 0

Reorder the terms:
4(-5 + a)(7 + a) = 0

Multiply (-5 + a) * (7 + a)
4(-5(7 + a) + a(7 + a)) = 0
4((7 * -5 + a * -5) + a(7 + a)) = 0
4((-35 + -5a) + a(7 + a)) = 0
4(-35 + -5a + (7 * a + a * a)) = 0
4(-35 + -5a + (7a + a2)) = 0

Combine like terms: -5a + 7a = 2a
4(-35 + 2a + a2) = 0
(-35 * 4 + 2a * 4 + a2 * 4) = 0
(-140 + 8a + 4a2) = 0

Solving
-140 + 8a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 2a + a2) = 0

Factor a trinomial.
4((-7 + -1a)(5 + -1a)) = 0

Ignore the factor 4.

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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-7, 5}

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