7x-3+15x-7+x^2-13=180

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Solution for 7x-3+15x-7+x^2-13=180 equation: 


Simplifying
7x + -3 + 15x + -7 + x2 + -13 = 180

Reorder the terms:
-3 + -7 + -13 + 7x + 15x + x2 = 180

Combine like terms: -3 + -7 = -10
-10 + -13 + 7x + 15x + x2 = 180

Combine like terms: -10 + -13 = -23
-23 + 7x + 15x + x2 = 180

Combine like terms: 7x + 15x = 22x
-23 + 22x + x2 = 180

Solving
-23 + 22x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-23 + -180 + 22x + x2 = 180 + -180

Combine like terms: -23 + -180 = -203
-203 + 22x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-203 + 22x + x2 = 0

Factor a trinomial.
(-29 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-29 + -1x)' equal to zero and attempt to solve:

Simplifying
-29 + -1x = 0

Solving
-29 + -1x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1x = 0 + 29
-1x = 0 + 29

Combine like terms: 0 + 29 = 29
-1x = 29

Divide each side by '-1'.
x = -29

Simplifying
x = -29

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-29, 7}

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