(x-10)(x-1)=(-14-5x)(x-1)

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Solution for (x-10)(x-1)=(-14-5x)(x-1) equation: 


Simplifying
(x + -10)(x + -1) = (-14 + -5x)(x + -1)

Reorder the terms:
(-10 + x)(x + -1) = (-14 + -5x)(x + -1)

Reorder the terms:
(-10 + x)(-1 + x) = (-14 + -5x)(x + -1)

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

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

Reorder the terms:
10 + -11x + x2 = (-14 + -5x)(-1 + x)

Multiply (-14 + -5x) * (-1 + x)
10 + -11x + x2 = (-14(-1 + x) + -5x * (-1 + x))
10 + -11x + x2 = ((-1 * -14 + x * -14) + -5x * (-1 + x))
10 + -11x + x2 = ((14 + -14x) + -5x * (-1 + x))
10 + -11x + x2 = (14 + -14x + (-1 * -5x + x * -5x))
10 + -11x + x2 = (14 + -14x + (5x + -5x2))

Combine like terms: -14x + 5x = -9x
10 + -11x + x2 = (14 + -9x + -5x2)

Solving
10 + -11x + x2 = 14 + -9x + -5x2

Solving for variable 'x'.

Reorder the terms:
10 + -14 + -11x + 9x + x2 + 5x2 = 14 + -9x + -5x2 + -14 + 9x + 5x2

Combine like terms: 10 + -14 = -4
-4 + -11x + 9x + x2 + 5x2 = 14 + -9x + -5x2 + -14 + 9x + 5x2

Combine like terms: -11x + 9x = -2x
-4 + -2x + x2 + 5x2 = 14 + -9x + -5x2 + -14 + 9x + 5x2

Combine like terms: x2 + 5x2 = 6x2
-4 + -2x + 6x2 = 14 + -9x + -5x2 + -14 + 9x + 5x2

Reorder the terms:
-4 + -2x + 6x2 = 14 + -14 + -9x + 9x + -5x2 + 5x2

Combine like terms: 14 + -14 = 0
-4 + -2x + 6x2 = 0 + -9x + 9x + -5x2 + 5x2
-4 + -2x + 6x2 = -9x + 9x + -5x2 + 5x2

Combine like terms: -9x + 9x = 0
-4 + -2x + 6x2 = 0 + -5x2 + 5x2
-4 + -2x + 6x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-4 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1x + 3x2) = 0

Factor a trinomial.
2((-2 + -3x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.6666666667, 1}

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