5x-3x(x+4)-(x-3)(2x+1)=0

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Solution for 5x-3x(x+4)-(x-3)(2x+1)=0 equation: 


Simplifying
5x + -3x(x + 4) + -1(x + -3)(2x + 1) = 0

Reorder the terms:
5x + -3x(4 + x) + -1(x + -3)(2x + 1) = 0
5x + (4 * -3x + x * -3x) + -1(x + -3)(2x + 1) = 0
5x + (-12x + -3x2) + -1(x + -3)(2x + 1) = 0

Reorder the terms:
5x + -12x + -3x2 + -1(-3 + x)(2x + 1) = 0

Reorder the terms:
5x + -12x + -3x2 + -1(-3 + x)(1 + 2x) = 0

Multiply (-3 + x) * (1 + 2x)
5x + -12x + -3x2 + -1(-3(1 + 2x) + x(1 + 2x)) = 0
5x + -12x + -3x2 + -1((1 * -3 + 2x * -3) + x(1 + 2x)) = 0
5x + -12x + -3x2 + -1((-3 + -6x) + x(1 + 2x)) = 0
5x + -12x + -3x2 + -1(-3 + -6x + (1 * x + 2x * x)) = 0
5x + -12x + -3x2 + -1(-3 + -6x + (1x + 2x2)) = 0

Combine like terms: -6x + 1x = -5x
5x + -12x + -3x2 + -1(-3 + -5x + 2x2) = 0
5x + -12x + -3x2 + (-3 * -1 + -5x * -1 + 2x2 * -1) = 0
5x + -12x + -3x2 + (3 + 5x + -2x2) = 0

Reorder the terms:
3 + 5x + -12x + 5x + -3x2 + -2x2 = 0

Combine like terms: 5x + -12x = -7x
3 + -7x + 5x + -3x2 + -2x2 = 0

Combine like terms: -7x + 5x = -2x
3 + -2x + -3x2 + -2x2 = 0

Combine like terms: -3x2 + -2x2 = -5x2
3 + -2x + -5x2 = 0

Solving
3 + -2x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -5x)(1 + x) = 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 '(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 = {0.6, -1}

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