8=4x(x-3)-(x-8)

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Solution for 8=4x(x-3)-(x-8) equation: 


Simplifying
8 = 4x(x + -3) + -1(x + -8)

Reorder the terms:
8 = 4x(-3 + x) + -1(x + -8)
8 = (-3 * 4x + x * 4x) + -1(x + -8)
8 = (-12x + 4x2) + -1(x + -8)

Reorder the terms:
8 = -12x + 4x2 + -1(-8 + x)
8 = -12x + 4x2 + (-8 * -1 + x * -1)
8 = -12x + 4x2 + (8 + -1x)

Reorder the terms:
8 = 8 + -12x + -1x + 4x2

Combine like terms: -12x + -1x = -13x
8 = 8 + -13x + 4x2

Add '-8' to each side of the equation.
8 + -8 = 8 + -13x + -8 + 4x2

Combine like terms: 8 + -8 = 0
0 = 8 + -13x + -8 + 4x2

Reorder the terms:
0 = 8 + -8 + -13x + 4x2

Combine like terms: 8 + -8 = 0
0 = 0 + -13x + 4x2
0 = -13x + 4x2

Solving
0 = -13x + 4x2

Solving for variable 'x'.
Remove the zero:
13x + -4x2 = -13x + 4x2 + 13x + -4x2

Reorder the terms:
13x + -4x2 = -13x + 13x + 4x2 + -4x2

Combine like terms: -13x + 13x = 0
13x + -4x2 = 0 + 4x2 + -4x2
13x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
13x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -4x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 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 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {0, 3.25}

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