0=x^2-10x-75

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Solution for 0=x^2-10x-75 equation:


Simplifying
0 = x2 + -10x + -75

Reorder the terms:
0 = -75 + -10x + x2

Solving
0 = -75 + -10x + x2

Solving for variable 'x'.

Combine like terms: 0 + 75 = 75
75 + 10x + -1x2 = -75 + -10x + x2 + 75 + 10x + -1x2

Reorder the terms:
75 + 10x + -1x2 = -75 + 75 + -10x + 10x + x2 + -1x2

Combine like terms: -75 + 75 = 0
75 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2
75 + 10x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
75 + 10x + -1x2 = 0 + x2 + -1x2
75 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
75 + 10x + -1x2 = 0

Factor a trinomial.
(15 + -1x)(5 + x) = 0

Subproblem 1

Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {15, -5}

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