(9x+8)*(5x+4)-(9x+8)*(3x-9)=0

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Solution for (9x+8)*(5x+4)-(9x+8)*(3x-9)=0 equation: 


Simplifying
(9x + 8)(5x + 4) + -1(9x + 8)(3x + -9) = 0

Reorder the terms:
(8 + 9x)(5x + 4) + -1(9x + 8)(3x + -9) = 0

Reorder the terms:
(8 + 9x)(4 + 5x) + -1(9x + 8)(3x + -9) = 0

Multiply (8 + 9x) * (4 + 5x)
(8(4 + 5x) + 9x * (4 + 5x)) + -1(9x + 8)(3x + -9) = 0
((4 * 8 + 5x * 8) + 9x * (4 + 5x)) + -1(9x + 8)(3x + -9) = 0
((32 + 40x) + 9x * (4 + 5x)) + -1(9x + 8)(3x + -9) = 0
(32 + 40x + (4 * 9x + 5x * 9x)) + -1(9x + 8)(3x + -9) = 0
(32 + 40x + (36x + 45x2)) + -1(9x + 8)(3x + -9) = 0

Combine like terms: 40x + 36x = 76x
(32 + 76x + 45x2) + -1(9x + 8)(3x + -9) = 0

Reorder the terms:
32 + 76x + 45x2 + -1(8 + 9x)(3x + -9) = 0

Reorder the terms:
32 + 76x + 45x2 + -1(8 + 9x)(-9 + 3x) = 0

Multiply (8 + 9x) * (-9 + 3x)
32 + 76x + 45x2 + -1(8(-9 + 3x) + 9x * (-9 + 3x)) = 0
32 + 76x + 45x2 + -1((-9 * 8 + 3x * 8) + 9x * (-9 + 3x)) = 0
32 + 76x + 45x2 + -1((-72 + 24x) + 9x * (-9 + 3x)) = 0
32 + 76x + 45x2 + -1(-72 + 24x + (-9 * 9x + 3x * 9x)) = 0
32 + 76x + 45x2 + -1(-72 + 24x + (-81x + 27x2)) = 0

Combine like terms: 24x + -81x = -57x
32 + 76x + 45x2 + -1(-72 + -57x + 27x2) = 0
32 + 76x + 45x2 + (-72 * -1 + -57x * -1 + 27x2 * -1) = 0
32 + 76x + 45x2 + (72 + 57x + -27x2) = 0

Reorder the terms:
32 + 72 + 76x + 57x + 45x2 + -27x2 = 0

Combine like terms: 32 + 72 = 104
104 + 76x + 57x + 45x2 + -27x2 = 0

Combine like terms: 76x + 57x = 133x
104 + 133x + 45x2 + -27x2 = 0

Combine like terms: 45x2 + -27x2 = 18x2
104 + 133x + 18x2 = 0

Solving
104 + 133x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + 2x)(8 + 9x) = 0


Subproblem 1
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
Set the factor '(8 + 9x)' equal to zero and attempt to solve:

Simplifying
8 + 9x = 0

Solving
8 + 9x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 9x = 0 + -8
9x = 0 + -8

Combine like terms: 0 + -8 = -8
9x = -8

Divide each side by '9'.
x = -0.8888888889

Simplifying
x = -0.8888888889
Solution
x = {-6.5, -0.8888888889}

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