=(3a-7)(2a+7)

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Solution for =(3a-7)(2a+7) equation: 


Simplifying
0 = (3a + -7)(2a + 7)

Reorder the terms:
0 = (-7 + 3a)(2a + 7)

Reorder the terms:
0 = (-7 + 3a)(7 + 2a)

Multiply (-7 + 3a) * (7 + 2a)
0 = (-7(7 + 2a) + 3a * (7 + 2a))
0 = ((7 * -7 + 2a * -7) + 3a * (7 + 2a))
0 = ((-49 + -14a) + 3a * (7 + 2a))
0 = (-49 + -14a + (7 * 3a + 2a * 3a))
0 = (-49 + -14a + (21a + 6a2))

Combine like terms: -14a + 21a = 7a
0 = (-49 + 7a + 6a2)

Solving
0 = -49 + 7a + 6a2

Solving for variable 'a'.

Combine like terms: 0 + 49 = 49
49 + -7a + -6a2 = -49 + 7a + 6a2 + 49 + -7a + -6a2

Reorder the terms:
49 + -7a + -6a2 = -49 + 49 + 7a + -7a + 6a2 + -6a2

Combine like terms: -49 + 49 = 0
49 + -7a + -6a2 = 0 + 7a + -7a + 6a2 + -6a2
49 + -7a + -6a2 = 7a + -7a + 6a2 + -6a2

Combine like terms: 7a + -7a = 0
49 + -7a + -6a2 = 0 + 6a2 + -6a2
49 + -7a + -6a2 = 6a2 + -6a2

Combine like terms: 6a2 + -6a2 = 0
49 + -7a + -6a2 = 0

Factor a trinomial.
(7 + -3a)(7 + 2a) = 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 '(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 = {2.333333333, -3.5}

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