180=52+5x+30+180-3x^2-4

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Solution for 180=52+5x+30+180-3x^2-4 equation:


Simplifying
180 = 52 + 5x + 30 + 180 + -3x2 + -4

Reorder the terms:
180 = 52 + 30 + 180 + -4 + 5x + -3x2

Combine like terms: 52 + 30 = 82
180 = 82 + 180 + -4 + 5x + -3x2

Combine like terms: 82 + 180 = 262
180 = 262 + -4 + 5x + -3x2

Combine like terms: 262 + -4 = 258
180 = 258 + 5x + -3x2

Solving
180 = 258 + 5x + -3x2

Solving for variable 'x'.

Combine like terms: 180 + -258 = -78
-78 + -5x + 3x2 = 258 + 5x + -3x2 + -258 + -5x + 3x2

Reorder the terms:
-78 + -5x + 3x2 = 258 + -258 + 5x + -5x + -3x2 + 3x2

Combine like terms: 258 + -258 = 0
-78 + -5x + 3x2 = 0 + 5x + -5x + -3x2 + 3x2
-78 + -5x + 3x2 = 5x + -5x + -3x2 + 3x2

Combine like terms: 5x + -5x = 0
-78 + -5x + 3x2 = 0 + -3x2 + 3x2
-78 + -5x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-78 + -5x + 3x2 = 0

Factor a trinomial.
(-13 + -3x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-13 + -3x)' equal to zero and attempt to solve: Simplifying -13 + -3x = 0 Solving -13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -3x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3x = 0 + 13 -3x = 0 + 13 Combine like terms: 0 + 13 = 13 -3x = 13 Divide each side by '-3'. x = -4.333333333 Simplifying x = -4.333333333

Subproblem 2

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

Solution

x = {-4.333333333, 6}

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