7(2a-7)(9a+5)=0

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Solution for 7(2a-7)(9a+5)=0 equation: 


Simplifying
7(2a + -7)(9a + 5) = 0

Reorder the terms:
7(-7 + 2a)(9a + 5) = 0

Reorder the terms:
7(-7 + 2a)(5 + 9a) = 0

Multiply (-7 + 2a) * (5 + 9a)
7(-7(5 + 9a) + 2a * (5 + 9a)) = 0
7((5 * -7 + 9a * -7) + 2a * (5 + 9a)) = 0
7((-35 + -63a) + 2a * (5 + 9a)) = 0
7(-35 + -63a + (5 * 2a + 9a * 2a)) = 0
7(-35 + -63a + (10a + 18a2)) = 0

Combine like terms: -63a + 10a = -53a
7(-35 + -53a + 18a2) = 0
(-35 * 7 + -53a * 7 + 18a2 * 7) = 0
(-245 + -371a + 126a2) = 0

Solving
-245 + -371a + 126a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-35 + -53a + 18a2) = 0

Factor a trinomial.
7((-5 + -9a)(7 + -2a)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-5 + -9a)' equal to zero and attempt to solve:

Simplifying
-5 + -9a = 0

Solving
-5 + -9a = 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 + -9a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9a = 0 + 5
-9a = 0 + 5

Combine like terms: 0 + 5 = 5
-9a = 5

Divide each side by '-9'.
a = -0.5555555556

Simplifying
a = -0.5555555556

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

Simplifying
7 + -2a = 0

Solving
7 + -2a = 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 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-0.5555555556, 3.5}

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