(x-8)(4x+1)=11(x-8)

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Solution for (x-8)(4x+1)=11(x-8) equation: 


Simplifying
(x + -8)(4x + 1) = 11(x + -8)

Reorder the terms:
(-8 + x)(4x + 1) = 11(x + -8)

Reorder the terms:
(-8 + x)(1 + 4x) = 11(x + -8)

Multiply (-8 + x) * (1 + 4x)
(-8(1 + 4x) + x(1 + 4x)) = 11(x + -8)
((1 * -8 + 4x * -8) + x(1 + 4x)) = 11(x + -8)
((-8 + -32x) + x(1 + 4x)) = 11(x + -8)
(-8 + -32x + (1 * x + 4x * x)) = 11(x + -8)
(-8 + -32x + (1x + 4x2)) = 11(x + -8)

Combine like terms: -32x + 1x = -31x
(-8 + -31x + 4x2) = 11(x + -8)

Reorder the terms:
-8 + -31x + 4x2 = 11(-8 + x)
-8 + -31x + 4x2 = (-8 * 11 + x * 11)
-8 + -31x + 4x2 = (-88 + 11x)

Solving
-8 + -31x + 4x2 = -88 + 11x

Solving for variable 'x'.

Reorder the terms:
-8 + 88 + -31x + -11x + 4x2 = -88 + 11x + 88 + -11x

Combine like terms: -8 + 88 = 80
80 + -31x + -11x + 4x2 = -88 + 11x + 88 + -11x

Combine like terms: -31x + -11x = -42x
80 + -42x + 4x2 = -88 + 11x + 88 + -11x

Reorder the terms:
80 + -42x + 4x2 = -88 + 88 + 11x + -11x

Combine like terms: -88 + 88 = 0
80 + -42x + 4x2 = 0 + 11x + -11x
80 + -42x + 4x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
80 + -42x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -21x + 2x2) = 0

Factor a trinomial.
2((5 + -2x)(8 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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 = {2.5, 8}

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