2x(x+5)+4=3x-x^2

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Solution for 2x(x+5)+4=3x-x^2 equation: 


Simplifying
2x(x + 5) + 4 = 3x + -1x2

Reorder the terms:
2x(5 + x) + 4 = 3x + -1x2
(5 * 2x + x * 2x) + 4 = 3x + -1x2
(10x + 2x2) + 4 = 3x + -1x2

Reorder the terms:
4 + 10x + 2x2 = 3x + -1x2

Solving
4 + 10x + 2x2 = 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
4 + 10x + -3x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: 10x + -3x = 7x
4 + 7x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: 2x2 + x2 = 3x2
4 + 7x + 3x2 = 3x + -1x2 + -3x + x2

Reorder the terms:
4 + 7x + 3x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
4 + 7x + 3x2 = 0 + -1x2 + x2
4 + 7x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
4 + 7x + 3x2 = 0

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


Subproblem 1
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, -1}

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