(2a-9)(3a+4a-4)=0

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Solution for (2a-9)(3a+4a-4)=0 equation:


Simplifying
(2a + -9)(3a + 4a + -4) = 0

Reorder the terms:
(-9 + 2a)(3a + 4a + -4) = 0

Reorder the terms:
(-9 + 2a)(-4 + 3a + 4a) = 0

Combine like terms: 3a + 4a = 7a
(-9 + 2a)(-4 + 7a) = 0

Multiply (-9 + 2a) * (-4 + 7a)
(-9(-4 + 7a) + 2a * (-4 + 7a)) = 0
((-4 * -9 + 7a * -9) + 2a * (-4 + 7a)) = 0
((36 + -63a) + 2a * (-4 + 7a)) = 0
(36 + -63a + (-4 * 2a + 7a * 2a)) = 0
(36 + -63a + (-8a + 14a2)) = 0

Combine like terms: -63a + -8a = -71a
(36 + -71a + 14a2) = 0

Solving
36 + -71a + 14a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -7a)(9 + -2a) = 0


Subproblem 1
Set the factor '(4 + -7a)' equal to zero and attempt to solve:

Simplifying
4 + -7a = 0

Solving
4 + -7a = 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 + -7a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7a = 0 + -4
-7a = 0 + -4

Combine like terms: 0 + -4 = -4
-7a = -4

Divide each side by '-7'.
a = 0.5714285714

Simplifying
a = 0.5714285714

Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve:

Simplifying
9 + -2a = 0

Solving
9 + -2a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2a = 0 + -9
-2a = 0 + -9

Combine like terms: 0 + -9 = -9
-2a = -9

Divide each side by '-2'.
a = 4.5

Simplifying
a = 4.5
Solution
a = {0.5714285714, 4.5}

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