(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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