5x(3x+2)+10x=20

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Solution for 5x(3x+2)+10x=20 equation: 


Simplifying
5x(3x + 2) + 10x = 20

Reorder the terms:
5x(2 + 3x) + 10x = 20
(2 * 5x + 3x * 5x) + 10x = 20
(10x + 15x2) + 10x = 20

Reorder the terms:
10x + 10x + 15x2 = 20

Combine like terms: 10x + 10x = 20x
20x + 15x2 = 20

Solving
20x + 15x2 = 20

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 4x + 3x2) = 0

Factor a trinomial.
5((-2 + -1x)(2 + -3x)) = 0

Ignore the factor 5.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-2, 0.6666666667}

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