(x-1)(x+5)=7

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Solution for (x-1)(x+5)=7 equation:


Simplifying
(x + -1)(x + 5) = 7

Reorder the terms:
(-1 + x)(x + 5) = 7

Reorder the terms:
(-1 + x)(5 + x) = 7

Multiply (-1 + x) * (5 + x)
(-1(5 + x) + x(5 + x)) = 7
((5 * -1 + x * -1) + x(5 + x)) = 7
((-5 + -1x) + x(5 + x)) = 7
(-5 + -1x + (5 * x + x * x)) = 7
(-5 + -1x + (5x + x2)) = 7

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) = 7

Solving
-5 + 4x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-5 + -7 + 4x + x2 = 7 + -7

Combine like terms: -5 + -7 = -12
-12 + 4x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-6, 2}

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