(x+1)(x-1)-3(x+2)=-7

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Solution for (x+1)(x-1)-3(x+2)=-7 equation:


Simplifying
(x + 1)(x + -1) + -3(x + 2) = -7

Reorder the terms:
(1 + x)(x + -1) + -3(x + 2) = -7

Reorder the terms:
(1 + x)(-1 + x) + -3(x + 2) = -7

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) + -3(x + 2) = -7
((-1 * 1 + x * 1) + x(-1 + x)) + -3(x + 2) = -7
((-1 + 1x) + x(-1 + x)) + -3(x + 2) = -7
(-1 + 1x + (-1 * x + x * x)) + -3(x + 2) = -7
(-1 + 1x + (-1x + x2)) + -3(x + 2) = -7

Combine like terms: 1x + -1x = 0
(-1 + 0 + x2) + -3(x + 2) = -7
(-1 + x2) + -3(x + 2) = -7

Reorder the terms:
-1 + x2 + -3(2 + x) = -7
-1 + x2 + (2 * -3 + x * -3) = -7
-1 + x2 + (-6 + -3x) = -7

Reorder the terms:
-1 + -6 + -3x + x2 = -7

Combine like terms: -1 + -6 = -7
-7 + -3x + x2 = -7

Add '7' to each side of the equation.
-7 + -3x + 7 + x2 = -7 + 7

Reorder the terms:
-7 + 7 + -3x + x2 = -7 + 7

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

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

Solving
-3x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, 3}

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