8x(x-4)-100=5x(x-9)

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Solution for 8x(x-4)-100=5x(x-9) equation: 


Simplifying
8x(x + -4) + -100 = 5x(x + -9)

Reorder the terms:
8x(-4 + x) + -100 = 5x(x + -9)
(-4 * 8x + x * 8x) + -100 = 5x(x + -9)
(-32x + 8x2) + -100 = 5x(x + -9)

Reorder the terms:
-100 + -32x + 8x2 = 5x(x + -9)

Reorder the terms:
-100 + -32x + 8x2 = 5x(-9 + x)
-100 + -32x + 8x2 = (-9 * 5x + x * 5x)
-100 + -32x + 8x2 = (-45x + 5x2)

Solving
-100 + -32x + 8x2 = -45x + 5x2

Solving for variable 'x'.

Reorder the terms:
-100 + -32x + 45x + 8x2 + -5x2 = -45x + 5x2 + 45x + -5x2

Combine like terms: -32x + 45x = 13x
-100 + 13x + 8x2 + -5x2 = -45x + 5x2 + 45x + -5x2

Combine like terms: 8x2 + -5x2 = 3x2
-100 + 13x + 3x2 = -45x + 5x2 + 45x + -5x2

Reorder the terms:
-100 + 13x + 3x2 = -45x + 45x + 5x2 + -5x2

Combine like terms: -45x + 45x = 0
-100 + 13x + 3x2 = 0 + 5x2 + -5x2
-100 + 13x + 3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-100 + 13x + 3x2 = 0

Factor a trinomial.
(-25 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-25 + -3x)' equal to zero and attempt to solve:

Simplifying
-25 + -3x = 0

Solving
-25 + -3x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -3x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -3x = 0 + 25
-3x = 0 + 25

Combine like terms: 0 + 25 = 25
-3x = 25

Divide each side by '-3'.
x = -8.333333333

Simplifying
x = -8.333333333

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-8.333333333, 4}

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