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

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


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

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

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

Combine like terms: 11 + -4 = 7
7 + -8x + 4x2 = 2x + 3

Reorder the terms:
7 + -8x + 4x2 = 3 + 2x

Solving
7 + -8x + 4x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
7 + -3 + -8x + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: 7 + -3 = 4
4 + -8x + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: -8x + -2x = -10x
4 + -10x + 4x2 = 3 + 2x + -3 + -2x

Reorder the terms:
4 + -10x + 4x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
4 + -10x + 4x2 = 0 + 2x + -2x
4 + -10x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5x + 2x2) = 0

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

Ignore the factor 2.

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 '(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 = {0.5, 2}

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