3(5+x^2)=x(5x-13)

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Solution for 3(5+x^2)=x(5x-13) equation: 


Simplifying
3(5 + x2) = x(5x + -13)
(5 * 3 + x2 * 3) = x(5x + -13)
(15 + 3x2) = x(5x + -13)

Reorder the terms:
15 + 3x2 = x(-13 + 5x)
15 + 3x2 = (-13 * x + 5x * x)
15 + 3x2 = (-13x + 5x2)

Solving
15 + 3x2 = -13x + 5x2

Solving for variable 'x'.

Reorder the terms:
15 + 13x + 3x2 + -5x2 = -13x + 5x2 + 13x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
15 + 13x + -2x2 = -13x + 5x2 + 13x + -5x2

Reorder the terms:
15 + 13x + -2x2 = -13x + 13x + 5x2 + -5x2

Combine like terms: -13x + 13x = 0
15 + 13x + -2x2 = 0 + 5x2 + -5x2
15 + 13x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
15 + 13x + -2x2 = 0

Factor a trinomial.
(15 + -2x)(1 + x) = 0


Subproblem 1
Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {7.5, -1}

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