(3x-11)(5x-4)=(x+2)(-x+17)

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Solution for (3x-11)(5x-4)=(x+2)(-x+17) equation: 


Simplifying
(3x + -11)(5x + -4) = (x + 2)(-1x + 17)

Reorder the terms:
(-11 + 3x)(5x + -4) = (x + 2)(-1x + 17)

Reorder the terms:
(-11 + 3x)(-4 + 5x) = (x + 2)(-1x + 17)

Multiply (-11 + 3x) * (-4 + 5x)
(-11(-4 + 5x) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17)
((-4 * -11 + 5x * -11) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17)
((44 + -55x) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17)
(44 + -55x + (-4 * 3x + 5x * 3x)) = (x + 2)(-1x + 17)
(44 + -55x + (-12x + 15x2)) = (x + 2)(-1x + 17)

Combine like terms: -55x + -12x = -67x
(44 + -67x + 15x2) = (x + 2)(-1x + 17)

Reorder the terms:
44 + -67x + 15x2 = (2 + x)(-1x + 17)

Reorder the terms:
44 + -67x + 15x2 = (2 + x)(17 + -1x)

Multiply (2 + x) * (17 + -1x)
44 + -67x + 15x2 = (2(17 + -1x) + x(17 + -1x))
44 + -67x + 15x2 = ((17 * 2 + -1x * 2) + x(17 + -1x))
44 + -67x + 15x2 = ((34 + -2x) + x(17 + -1x))
44 + -67x + 15x2 = (34 + -2x + (17 * x + -1x * x))
44 + -67x + 15x2 = (34 + -2x + (17x + -1x2))

Combine like terms: -2x + 17x = 15x
44 + -67x + 15x2 = (34 + 15x + -1x2)

Solving
44 + -67x + 15x2 = 34 + 15x + -1x2

Solving for variable 'x'.

Reorder the terms:
44 + -34 + -67x + -15x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2

Combine like terms: 44 + -34 = 10
10 + -67x + -15x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2

Combine like terms: -67x + -15x = -82x
10 + -82x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2

Combine like terms: 15x2 + x2 = 16x2
10 + -82x + 16x2 = 34 + 15x + -1x2 + -34 + -15x + x2

Reorder the terms:
10 + -82x + 16x2 = 34 + -34 + 15x + -15x + -1x2 + x2

Combine like terms: 34 + -34 = 0
10 + -82x + 16x2 = 0 + 15x + -15x + -1x2 + x2
10 + -82x + 16x2 = 15x + -15x + -1x2 + x2

Combine like terms: 15x + -15x = 0
10 + -82x + 16x2 = 0 + -1x2 + x2
10 + -82x + 16x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10 + -82x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -41x + 8x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -8x = 0

Solving
1 + -8x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8x = 0 + -1

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

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

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.125, 5}

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