10-2x(2x+1)=4(x-2)

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Solution for 10-2x(2x+1)=4(x-2) equation: 


Simplifying
10 + -2x(2x + 1) = 4(x + -2)

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

Reorder the terms:
10 + -2x + -4x2 = 4(-2 + x)
10 + -2x + -4x2 = (-2 * 4 + x * 4)
10 + -2x + -4x2 = (-8 + 4x)

Solving
10 + -2x + -4x2 = -8 + 4x

Solving for variable 'x'.

Reorder the terms:
10 + 8 + -2x + -4x + -4x2 = -8 + 4x + 8 + -4x

Combine like terms: 10 + 8 = 18
18 + -2x + -4x + -4x2 = -8 + 4x + 8 + -4x

Combine like terms: -2x + -4x = -6x
18 + -6x + -4x2 = -8 + 4x + 8 + -4x

Reorder the terms:
18 + -6x + -4x2 = -8 + 8 + 4x + -4x

Combine like terms: -8 + 8 = 0
18 + -6x + -4x2 = 0 + 4x + -4x
18 + -6x + -4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
18 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -3x + -2x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {1.5, -3}

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