(x+10)(x-1)=2(x-5)-12

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Solution for (x+10)(x-1)=2(x-5)-12 equation:


Simplifying
(x + 10)(x + -1) = 2(x + -5) + -12

Reorder the terms:
(10 + x)(x + -1) = 2(x + -5) + -12

Reorder the terms:
(10 + x)(-1 + x) = 2(x + -5) + -12

Multiply (10 + x) * (-1 + x)
(10(-1 + x) + x(-1 + x)) = 2(x + -5) + -12
((-1 * 10 + x * 10) + x(-1 + x)) = 2(x + -5) + -12
((-10 + 10x) + x(-1 + x)) = 2(x + -5) + -12
(-10 + 10x + (-1 * x + x * x)) = 2(x + -5) + -12
(-10 + 10x + (-1x + x2)) = 2(x + -5) + -12

Combine like terms: 10x + -1x = 9x
(-10 + 9x + x2) = 2(x + -5) + -12

Reorder the terms:
-10 + 9x + x2 = 2(-5 + x) + -12
-10 + 9x + x2 = (-5 * 2 + x * 2) + -12
-10 + 9x + x2 = (-10 + 2x) + -12

Reorder the terms:
-10 + 9x + x2 = -10 + -12 + 2x

Combine like terms: -10 + -12 = -22
-10 + 9x + x2 = -22 + 2x

Solving
-10 + 9x + x2 = -22 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + 22 + 9x + -2x + x2 = -22 + 2x + 22 + -2x

Combine like terms: -10 + 22 = 12
12 + 9x + -2x + x2 = -22 + 2x + 22 + -2x

Combine like terms: 9x + -2x = 7x
12 + 7x + x2 = -22 + 2x + 22 + -2x

Reorder the terms:
12 + 7x + x2 = -22 + 22 + 2x + -2x

Combine like terms: -22 + 22 = 0
12 + 7x + x2 = 0 + 2x + -2x
12 + 7x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
12 + 7x + x2 = 0

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

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-4, -3}

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