(x^2+34)+(6x+4)+(10x+10)=180

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Solution for (x^2+34)+(6x+4)+(10x+10)=180 equation:


Simplifying
(x2 + 34) + (6x + 4) + (10x + 10) = 180

Reorder the terms:
(34 + x2) + (6x + 4) + (10x + 10) = 180

Remove parenthesis around (34 + x2)
34 + x2 + (6x + 4) + (10x + 10) = 180

Reorder the terms:
34 + x2 + (4 + 6x) + (10x + 10) = 180

Remove parenthesis around (4 + 6x)
34 + x2 + 4 + 6x + (10x + 10) = 180

Reorder the terms:
34 + x2 + 4 + 6x + (10 + 10x) = 180

Remove parenthesis around (10 + 10x)
34 + x2 + 4 + 6x + 10 + 10x = 180

Reorder the terms:
34 + 4 + 10 + 6x + 10x + x2 = 180

Combine like terms: 34 + 4 = 38
38 + 10 + 6x + 10x + x2 = 180

Combine like terms: 38 + 10 = 48
48 + 6x + 10x + x2 = 180

Combine like terms: 6x + 10x = 16x
48 + 16x + x2 = 180

Solving
48 + 16x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
48 + -180 + 16x + x2 = 180 + -180

Combine like terms: 48 + -180 = -132
-132 + 16x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-132 + 16x + x2 = 0

Factor a trinomial.
(-22 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

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 = {-22, 6}

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