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

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


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

Reorder the terms:
(5 + 2x)(3x + -2) = 20

Reorder the terms:
(5 + 2x)(-2 + 3x) = 20

Multiply (5 + 2x) * (-2 + 3x)
(5(-2 + 3x) + 2x * (-2 + 3x)) = 20
((-2 * 5 + 3x * 5) + 2x * (-2 + 3x)) = 20
((-10 + 15x) + 2x * (-2 + 3x)) = 20
(-10 + 15x + (-2 * 2x + 3x * 2x)) = 20
(-10 + 15x + (-4x + 6x2)) = 20

Combine like terms: 15x + -4x = 11x
(-10 + 11x + 6x2) = 20

Solving
-10 + 11x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
-10 + -20 + 11x + 6x2 = 20 + -20

Combine like terms: -10 + -20 = -30
-30 + 11x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-30 + 11x + 6x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3.333333333, 1.5}

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