(3x^2-15)+(x^2+x)=90

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Solution for (3x^2-15)+(x^2+x)=90 equation: 


Simplifying
(3x2 + -15) + (x2 + x) = 90

Reorder the terms:
(-15 + 3x2) + (x2 + x) = 90

Remove parenthesis around (-15 + 3x2)
-15 + 3x2 + (x2 + x) = 90

Reorder the terms:
-15 + 3x2 + (x + x2) = 90

Remove parenthesis around (x + x2)
-15 + 3x2 + x + x2 = 90

Reorder the terms:
-15 + x + 3x2 + x2 = 90

Combine like terms: 3x2 + x2 = 4x2
-15 + x + 4x2 = 90

Solving
-15 + x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
-15 + -90 + x + 4x2 = 90 + -90

Combine like terms: -15 + -90 = -105
-105 + x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-105 + x + 4x2 = 0

Factor a trinomial.
(-21 + -4x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-21 + -4x)' equal to zero and attempt to solve:

Simplifying
-21 + -4x = 0

Solving
-21 + -4x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4x = 0 + 21
-4x = 0 + 21

Combine like terms: 0 + 21 = 21
-4x = 21

Divide each side by '-4'.
x = -5.25

Simplifying
x = -5.25

Subproblem 2
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
Solution
x = {-5.25, 5}

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