x^2-7x+120=180

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Solution for x^2-7x+120=180 equation:


Simplifying
x2 + -7x + 120 = 180

Reorder the terms:
120 + -7x + x2 = 180

Solving
120 + -7x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
120 + -180 + -7x + x2 = 180 + -180

Combine like terms: 120 + -180 = -60
-60 + -7x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-60 + -7x + x2 = 0

Factor a trinomial.
(-5 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 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 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12

Solution

x = {-5, 12}

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