(x+5)(x-7)=0

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Solution for (x+5)(x-7)=0 equation:


Simplifying
(x + 5)(x + -7) = 0

Reorder the terms:
(5 + x)(x + -7) = 0

Reorder the terms:
(5 + x)(-7 + x) = 0

Multiply (5 + x) * (-7 + x)
(5(-7 + x) + x(-7 + x)) = 0
((-7 * 5 + x * 5) + x(-7 + x)) = 0
((-35 + 5x) + x(-7 + x)) = 0
(-35 + 5x + (-7 * x + x * x)) = 0
(-35 + 5x + (-7x + x2)) = 0

Combine like terms: 5x + -7x = -2x
(-35 + -2x + x2) = 0

Solving
-35 + -2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-5, 7}

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