2x(2x+1)=20-5(x-2)

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Solution for 2x(2x+1)=20-5(x-2) equation: 


Simplifying
2x(2x + 1) = 20 + -5(x + -2)

Reorder the terms:
2x(1 + 2x) = 20 + -5(x + -2)
(1 * 2x + 2x * 2x) = 20 + -5(x + -2)
(2x + 4x2) = 20 + -5(x + -2)

Reorder the terms:
2x + 4x2 = 20 + -5(-2 + x)
2x + 4x2 = 20 + (-2 * -5 + x * -5)
2x + 4x2 = 20 + (10 + -5x)

Combine like terms: 20 + 10 = 30
2x + 4x2 = 30 + -5x

Solving
2x + 4x2 = 30 + -5x

Solving for variable 'x'.

Reorder the terms:
-30 + 2x + 5x + 4x2 = 30 + -5x + -30 + 5x

Combine like terms: 2x + 5x = 7x
-30 + 7x + 4x2 = 30 + -5x + -30 + 5x

Reorder the terms:
-30 + 7x + 4x2 = 30 + -30 + -5x + 5x

Combine like terms: 30 + -30 = 0
-30 + 7x + 4x2 = 0 + -5x + 5x
-30 + 7x + 4x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-30 + 7x + 4x2 = 0

Factor a trinomial.
(-15 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -4x)' equal to zero and attempt to solve:

Simplifying
-15 + -4x = 0

Solving
-15 + -4x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4x = 0 + 15
-4x = 0 + 15

Combine like terms: 0 + 15 = 15
-4x = 15

Divide each side by '-4'.
x = -3.75

Simplifying
x = -3.75

Subproblem 2
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
Solution
x = {-3.75, 2}

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