2(x^2-4)-3x=4x-11

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Solution for 2(x^2-4)-3x=4x-11 equation: 


Simplifying
2(x2 + -4) + -3x = 4x + -11

Reorder the terms:
2(-4 + x2) + -3x = 4x + -11
(-4 * 2 + x2 * 2) + -3x = 4x + -11
(-8 + 2x2) + -3x = 4x + -11

Reorder the terms:
-8 + -3x + 2x2 = 4x + -11

Reorder the terms:
-8 + -3x + 2x2 = -11 + 4x

Solving
-8 + -3x + 2x2 = -11 + 4x

Solving for variable 'x'.

Reorder the terms:
-8 + 11 + -3x + -4x + 2x2 = -11 + 4x + 11 + -4x

Combine like terms: -8 + 11 = 3
3 + -3x + -4x + 2x2 = -11 + 4x + 11 + -4x

Combine like terms: -3x + -4x = -7x
3 + -7x + 2x2 = -11 + 4x + 11 + -4x

Reorder the terms:
3 + -7x + 2x2 = -11 + 11 + 4x + -4x

Combine like terms: -11 + 11 = 0
3 + -7x + 2x2 = 0 + 4x + -4x
3 + -7x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
3 + -7x + 2x2 = 0

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


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}

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