(x+2)(x-5)+(x-1)=1(x+5)(x-5)

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


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

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

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

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

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) + (x + -1) = 1(x + 5)(x + -5)

Reorder the terms:
-10 + -3x + x2 + (-1 + x) = 1(x + 5)(x + -5)

Remove parenthesis around (-1 + x)
-10 + -3x + x2 + -1 + x = 1(x + 5)(x + -5)

Reorder the terms:
-10 + -1 + -3x + x + x2 = 1(x + 5)(x + -5)

Combine like terms: -10 + -1 = -11
-11 + -3x + x + x2 = 1(x + 5)(x + -5)

Combine like terms: -3x + x = -2x
-11 + -2x + x2 = 1(x + 5)(x + -5)

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

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

Multiply (5 + x) * (-5 + x)
-11 + -2x + x2 = 1(5(-5 + x) + x(-5 + x))
-11 + -2x + x2 = 1((-5 * 5 + x * 5) + x(-5 + x))
-11 + -2x + x2 = 1((-25 + 5x) + x(-5 + x))
-11 + -2x + x2 = 1(-25 + 5x + (-5 * x + x * x))
-11 + -2x + x2 = 1(-25 + 5x + (-5x + x2))

Combine like terms: 5x + -5x = 0
-11 + -2x + x2 = 1(-25 + 0 + x2)
-11 + -2x + x2 = 1(-25 + x2)
-11 + -2x + x2 = (-25 * 1 + x2 * 1)
-11 + -2x + x2 = (-25 + 1x2)

Solving
-11 + -2x + x2 = -25 + 1x2

Solving for variable 'x'.

Reorder the terms:
-11 + 25 + -2x + x2 + -1x2 = -25 + 1x2 + 25 + -1x2

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

Combine like terms: x2 + -1x2 = 0
14 + -2x + 0 = -25 + 1x2 + 25 + -1x2
14 + -2x = -25 + 1x2 + 25 + -1x2

Reorder the terms:
14 + -2x = -25 + 25 + 1x2 + -1x2

Combine like terms: -25 + 25 = 0
14 + -2x = 0 + 1x2 + -1x2
14 + -2x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
14 + -2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -1x) = 0

Ignore the factor 2.

Subproblem 1
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 = {7}

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