(2x-1)(x-5)=-x(x-14)-23

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Solution for (2x-1)(x-5)=-x(x-14)-23 equation: 


Simplifying
(2x + -1)(x + -5) = -1x(x + -14) + -23

Reorder the terms:
(-1 + 2x)(x + -5) = -1x(x + -14) + -23

Reorder the terms:
(-1 + 2x)(-5 + x) = -1x(x + -14) + -23

Multiply (-1 + 2x) * (-5 + x)
(-1(-5 + x) + 2x * (-5 + x)) = -1x(x + -14) + -23
((-5 * -1 + x * -1) + 2x * (-5 + x)) = -1x(x + -14) + -23
((5 + -1x) + 2x * (-5 + x)) = -1x(x + -14) + -23
(5 + -1x + (-5 * 2x + x * 2x)) = -1x(x + -14) + -23
(5 + -1x + (-10x + 2x2)) = -1x(x + -14) + -23

Combine like terms: -1x + -10x = -11x
(5 + -11x + 2x2) = -1x(x + -14) + -23

Reorder the terms:
5 + -11x + 2x2 = -1x(-14 + x) + -23
5 + -11x + 2x2 = (-14 * -1x + x * -1x) + -23
5 + -11x + 2x2 = (14x + -1x2) + -23

Reorder the terms:
5 + -11x + 2x2 = -23 + 14x + -1x2

Solving
5 + -11x + 2x2 = -23 + 14x + -1x2

Solving for variable 'x'.

Reorder the terms:
5 + 23 + -11x + -14x + 2x2 + x2 = -23 + 14x + -1x2 + 23 + -14x + x2

Combine like terms: 5 + 23 = 28
28 + -11x + -14x + 2x2 + x2 = -23 + 14x + -1x2 + 23 + -14x + x2

Combine like terms: -11x + -14x = -25x
28 + -25x + 2x2 + x2 = -23 + 14x + -1x2 + 23 + -14x + x2

Combine like terms: 2x2 + x2 = 3x2
28 + -25x + 3x2 = -23 + 14x + -1x2 + 23 + -14x + x2

Reorder the terms:
28 + -25x + 3x2 = -23 + 23 + 14x + -14x + -1x2 + x2

Combine like terms: -23 + 23 = 0
28 + -25x + 3x2 = 0 + 14x + -14x + -1x2 + x2
28 + -25x + 3x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
28 + -25x + 3x2 = 0 + -1x2 + x2
28 + -25x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
28 + -25x + 3x2 = 0

Factor a trinomial.
(4 + -3x)(7 + -1x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1.333333333, 7}

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