0=x^2+7x-60

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Solution for 0=x^2+7x-60 equation:


Simplifying
0 = x2 + 7x + -60

Reorder the terms:
0 = -60 + 7x + x2

Solving
0 = -60 + 7x + x2

Solving for variable 'x'.

Combine like terms: 0 + 60 = 60
60 + -7x + -1x2 = -60 + 7x + x2 + 60 + -7x + -1x2

Reorder the terms:
60 + -7x + -1x2 = -60 + 60 + 7x + -7x + x2 + -1x2

Combine like terms: -60 + 60 = 0
60 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
60 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
60 + -7x + -1x2 = 0 + x2 + -1x2
60 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -7x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(12 + x) = 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12

Solution

x = {5, -12}

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