(x^2+5x)+(-60-3x)=60

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Solution for (x^2+5x)+(-60-3x)=60 equation:


Simplifying
(x2 + 5x) + (-60 + -3x) = 60

Reorder the terms:
(5x + x2) + (-60 + -3x) = 60

Remove parenthesis around (5x + x2)
5x + x2 + (-60 + -3x) = 60

Remove parenthesis around (-60 + -3x)
5x + x2 + -60 + -3x = 60

Reorder the terms:
-60 + 5x + -3x + x2 = 60

Combine like terms: 5x + -3x = 2x
-60 + 2x + x2 = 60

Solving
-60 + 2x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -60 + 2x + x2 = 60 + -60

Combine like terms: -60 + -60 = -120
-120 + 2x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-120 + 2x + x2 = 0

Factor a trinomial.
(-12 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-12, 10}

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