3x+3=-5x^2+20x+15

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Solution for 3x+3=-5x^2+20x+15 equation: 


Simplifying
3x + 3 = -5x2 + 20x + 15

Reorder the terms:
3 + 3x = -5x2 + 20x + 15

Reorder the terms:
3 + 3x = 15 + 20x + -5x2

Solving
3 + 3x = 15 + 20x + -5x2

Solving for variable 'x'.

Reorder the terms:
3 + -15 + 3x + -20x + 5x2 = 15 + 20x + -5x2 + -15 + -20x + 5x2

Combine like terms: 3 + -15 = -12
-12 + 3x + -20x + 5x2 = 15 + 20x + -5x2 + -15 + -20x + 5x2

Combine like terms: 3x + -20x = -17x
-12 + -17x + 5x2 = 15 + 20x + -5x2 + -15 + -20x + 5x2

Reorder the terms:
-12 + -17x + 5x2 = 15 + -15 + 20x + -20x + -5x2 + 5x2

Combine like terms: 15 + -15 = 0
-12 + -17x + 5x2 = 0 + 20x + -20x + -5x2 + 5x2
-12 + -17x + 5x2 = 20x + -20x + -5x2 + 5x2

Combine like terms: 20x + -20x = 0
-12 + -17x + 5x2 = 0 + -5x2 + 5x2
-12 + -17x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-12 + -17x + 5x2 = 0

Factor a trinomial.
(-3 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.6, 4}

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