(x-8)(4x+5)-(x-8)(2x-4)=0

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Solution for (x-8)(4x+5)-(x-8)(2x-4)=0 equation: 


Simplifying
(x + -8)(4x + 5) + -1(x + -8)(2x + -4) = 0

Reorder the terms:
(-8 + x)(4x + 5) + -1(x + -8)(2x + -4) = 0

Reorder the terms:
(-8 + x)(5 + 4x) + -1(x + -8)(2x + -4) = 0

Multiply (-8 + x) * (5 + 4x)
(-8(5 + 4x) + x(5 + 4x)) + -1(x + -8)(2x + -4) = 0
((5 * -8 + 4x * -8) + x(5 + 4x)) + -1(x + -8)(2x + -4) = 0
((-40 + -32x) + x(5 + 4x)) + -1(x + -8)(2x + -4) = 0
(-40 + -32x + (5 * x + 4x * x)) + -1(x + -8)(2x + -4) = 0
(-40 + -32x + (5x + 4x2)) + -1(x + -8)(2x + -4) = 0

Combine like terms: -32x + 5x = -27x
(-40 + -27x + 4x2) + -1(x + -8)(2x + -4) = 0

Reorder the terms:
-40 + -27x + 4x2 + -1(-8 + x)(2x + -4) = 0

Reorder the terms:
-40 + -27x + 4x2 + -1(-8 + x)(-4 + 2x) = 0

Multiply (-8 + x) * (-4 + 2x)
-40 + -27x + 4x2 + -1(-8(-4 + 2x) + x(-4 + 2x)) = 0
-40 + -27x + 4x2 + -1((-4 * -8 + 2x * -8) + x(-4 + 2x)) = 0
-40 + -27x + 4x2 + -1((32 + -16x) + x(-4 + 2x)) = 0
-40 + -27x + 4x2 + -1(32 + -16x + (-4 * x + 2x * x)) = 0
-40 + -27x + 4x2 + -1(32 + -16x + (-4x + 2x2)) = 0

Combine like terms: -16x + -4x = -20x
-40 + -27x + 4x2 + -1(32 + -20x + 2x2) = 0
-40 + -27x + 4x2 + (32 * -1 + -20x * -1 + 2x2 * -1) = 0
-40 + -27x + 4x2 + (-32 + 20x + -2x2) = 0

Reorder the terms:
-40 + -32 + -27x + 20x + 4x2 + -2x2 = 0

Combine like terms: -40 + -32 = -72
-72 + -27x + 20x + 4x2 + -2x2 = 0

Combine like terms: -27x + 20x = -7x
-72 + -7x + 4x2 + -2x2 = 0

Combine like terms: 4x2 + -2x2 = 2x2
-72 + -7x + 2x2 = 0

Solving
-72 + -7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

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

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

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

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

Simplifying
x = -4.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-4.5, 8}

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