(x-1)(2x+5)+(x-1)2=0

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Solution for (x-1)(2x+5)+(x-1)2=0 equation: 


Simplifying
(x + -1)(2x + 5) + (x + -1) * 2 = 0

Reorder the terms:
(-1 + x)(2x + 5) + (x + -1) * 2 = 0

Reorder the terms:
(-1 + x)(5 + 2x) + (x + -1) * 2 = 0

Multiply (-1 + x) * (5 + 2x)
(-1(5 + 2x) + x(5 + 2x)) + (x + -1) * 2 = 0
((5 * -1 + 2x * -1) + x(5 + 2x)) + (x + -1) * 2 = 0
((-5 + -2x) + x(5 + 2x)) + (x + -1) * 2 = 0
(-5 + -2x + (5 * x + 2x * x)) + (x + -1) * 2 = 0
(-5 + -2x + (5x + 2x2)) + (x + -1) * 2 = 0

Combine like terms: -2x + 5x = 3x
(-5 + 3x + 2x2) + (x + -1) * 2 = 0

Reorder the terms:
-5 + 3x + 2x2 + (-1 + x) * 2 = 0

Reorder the terms for easier multiplication:
-5 + 3x + 2x2 + 2(-1 + x) = 0
-5 + 3x + 2x2 + (-1 * 2 + x * 2) = 0
-5 + 3x + 2x2 + (-2 + 2x) = 0

Reorder the terms:
-5 + -2 + 3x + 2x + 2x2 = 0

Combine like terms: -5 + -2 = -7
-7 + 3x + 2x + 2x2 = 0

Combine like terms: 3x + 2x = 5x
-7 + 5x + 2x2 = 0

Solving
-7 + 5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(1 + -1x) = 0


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

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 1}

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