8(x+5)+8(x-2)=9(x+5)(x-2)

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Solution for 8(x+5)+8(x-2)=9(x+5)(x-2) equation: 


Simplifying
8(x + 5) + 8(x + -2) = 9(x + 5)(x + -2)

Reorder the terms:
8(5 + x) + 8(x + -2) = 9(x + 5)(x + -2)
(5 * 8 + x * 8) + 8(x + -2) = 9(x + 5)(x + -2)
(40 + 8x) + 8(x + -2) = 9(x + 5)(x + -2)

Reorder the terms:
40 + 8x + 8(-2 + x) = 9(x + 5)(x + -2)
40 + 8x + (-2 * 8 + x * 8) = 9(x + 5)(x + -2)
40 + 8x + (-16 + 8x) = 9(x + 5)(x + -2)

Reorder the terms:
40 + -16 + 8x + 8x = 9(x + 5)(x + -2)

Combine like terms: 40 + -16 = 24
24 + 8x + 8x = 9(x + 5)(x + -2)

Combine like terms: 8x + 8x = 16x
24 + 16x = 9(x + 5)(x + -2)

Reorder the terms:
24 + 16x = 9(5 + x)(x + -2)

Reorder the terms:
24 + 16x = 9(5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
24 + 16x = 9(5(-2 + x) + x(-2 + x))
24 + 16x = 9((-2 * 5 + x * 5) + x(-2 + x))
24 + 16x = 9((-10 + 5x) + x(-2 + x))
24 + 16x = 9(-10 + 5x + (-2 * x + x * x))
24 + 16x = 9(-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
24 + 16x = 9(-10 + 3x + x2)
24 + 16x = (-10 * 9 + 3x * 9 + x2 * 9)
24 + 16x = (-90 + 27x + 9x2)

Solving
24 + 16x = -90 + 27x + 9x2

Solving for variable 'x'.

Reorder the terms:
24 + 90 + 16x + -27x + -9x2 = -90 + 27x + 9x2 + 90 + -27x + -9x2

Combine like terms: 24 + 90 = 114
114 + 16x + -27x + -9x2 = -90 + 27x + 9x2 + 90 + -27x + -9x2

Combine like terms: 16x + -27x = -11x
114 + -11x + -9x2 = -90 + 27x + 9x2 + 90 + -27x + -9x2

Reorder the terms:
114 + -11x + -9x2 = -90 + 90 + 27x + -27x + 9x2 + -9x2

Combine like terms: -90 + 90 = 0
114 + -11x + -9x2 = 0 + 27x + -27x + 9x2 + -9x2
114 + -11x + -9x2 = 27x + -27x + 9x2 + -9x2

Combine like terms: 27x + -27x = 0
114 + -11x + -9x2 = 0 + 9x2 + -9x2
114 + -11x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
114 + -11x + -9x2 = 0

Factor a trinomial.
(3 + -1x)(38 + 9x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(38 + 9x)' equal to zero and attempt to solve:

Simplifying
38 + 9x = 0

Solving
38 + 9x = 0

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

Add '-38' to each side of the equation.
38 + -38 + 9x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 9x = 0 + -38
9x = 0 + -38

Combine like terms: 0 + -38 = -38
9x = -38

Divide each side by '9'.
x = -4.222222222

Simplifying
x = -4.222222222
Solution
x = {3, -4.222222222}

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