3(4x-3)+4(1+2x)(1+2x)=16(x-2)21345

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Solution for 3(4x-3)+4(1+2x)(1+2x)=16(x-2)21345 equation:


Simplifying
3(4x + -3) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 21345

Reorder the terms:
3(-3 + 4x) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 21345
(-3 * 3 + 4x * 3) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 21345
(-9 + 12x) + 4(1 + 2x)(1 + 2x) = 16(x + -2) * 21345

Multiply (1 + 2x) * (1 + 2x)
-9 + 12x + 4(1(1 + 2x) + 2x * (1 + 2x)) = 16(x + -2) * 21345
-9 + 12x + 4((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 16(x + -2) * 21345
-9 + 12x + 4((1 + 2x) + 2x * (1 + 2x)) = 16(x + -2) * 21345
-9 + 12x + 4(1 + 2x + (1 * 2x + 2x * 2x)) = 16(x + -2) * 21345
-9 + 12x + 4(1 + 2x + (2x + 4x2)) = 16(x + -2) * 21345

Combine like terms: 2x + 2x = 4x
-9 + 12x + 4(1 + 4x + 4x2) = 16(x + -2) * 21345
-9 + 12x + (1 * 4 + 4x * 4 + 4x2 * 4) = 16(x + -2) * 21345
-9 + 12x + (4 + 16x + 16x2) = 16(x + -2) * 21345

Reorder the terms:
-9 + 4 + 12x + 16x + 16x2 = 16(x + -2) * 21345

Combine like terms: -9 + 4 = -5
-5 + 12x + 16x + 16x2 = 16(x + -2) * 21345

Combine like terms: 12x + 16x = 28x
-5 + 28x + 16x2 = 16(x + -2) * 21345

Reorder the terms:
-5 + 28x + 16x2 = 16(-2 + x) * 21345

Reorder the terms for easier multiplication:
-5 + 28x + 16x2 = 16 * 21345(-2 + x)

Multiply 16 * 21345
-5 + 28x + 16x2 = 341520(-2 + x)
-5 + 28x + 16x2 = (-2 * 341520 + x * 341520)
-5 + 28x + 16x2 = (-683040 + 341520x)

Solving
-5 + 28x + 16x2 = -683040 + 341520x

Solving for variable 'x'.

Reorder the terms:
-5 + 683040 + 28x + -341520x + 16x2 = -683040 + 341520x + 683040 + -341520x

Combine like terms: -5 + 683040 = 683035
683035 + 28x + -341520x + 16x2 = -683040 + 341520x + 683040 + -341520x

Combine like terms: 28x + -341520x = -341492x
683035 + -341492x + 16x2 = -683040 + 341520x + 683040 + -341520x

Reorder the terms:
683035 + -341492x + 16x2 = -683040 + 683040 + 341520x + -341520x

Combine like terms: -683040 + 683040 = 0
683035 + -341492x + 16x2 = 0 + 341520x + -341520x
683035 + -341492x + 16x2 = 341520x + -341520x

Combine like terms: 341520x + -341520x = 0
683035 + -341492x + 16x2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
42689.6875 + -21343.25x + x2 = 0

Move the constant term to the right:

Add '-42689.6875' to each side of the equation.
42689.6875 + -21343.25x + -42689.6875 + x2 = 0 + -42689.6875

Reorder the terms:
42689.6875 + -42689.6875 + -21343.25x + x2 = 0 + -42689.6875

Combine like terms: 42689.6875 + -42689.6875 = 0.0000
0.0000 + -21343.25x + x2 = 0 + -42689.6875
-21343.25x + x2 = 0 + -42689.6875

Combine like terms: 0 + -42689.6875 = -42689.6875
-21343.25x + x2 = -42689.6875

The x term is -21343.25x.  Take half its coefficient (-10671.625).
Square it (113883580.1) and add it to both sides.

Add '113883580.1' to each side of the equation.
-21343.25x + 113883580.1 + x2 = -42689.6875 + 113883580.1

Reorder the terms:
113883580.1 + -21343.25x + x2 = -42689.6875 + 113883580.1

Combine like terms: -42689.6875 + 113883580.1 = 113840890.4125
113883580.1 + -21343.25x + x2 = 113840890.4125

Factor a perfect square on the left side:
(x + -10671.625)(x + -10671.625) = 113840890.4125

Calculate the square root of the right side: 10669.624661276

Break this problem into two subproblems by setting 
(x + -10671.625) equal to 10669.624661276 and -10669.624661276.

Subproblem 1

x + -10671.625 = 10669.624661276 Simplifying x + -10671.625 = 10669.624661276 Reorder the terms: -10671.625 + x = 10669.624661276 Solving -10671.625 + x = 10669.624661276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10671.625' to each side of the equation. -10671.625 + 10671.625 + x = 10669.624661276 + 10671.625 Combine like terms: -10671.625 + 10671.625 = 0.000 0.000 + x = 10669.624661276 + 10671.625 x = 10669.624661276 + 10671.625 Combine like terms: 10669.624661276 + 10671.625 = 21341.249661276 x = 21341.249661276 Simplifying x = 21341.249661276

Subproblem 2

x + -10671.625 = -10669.624661276 Simplifying x + -10671.625 = -10669.624661276 Reorder the terms: -10671.625 + x = -10669.624661276 Solving -10671.625 + x = -10669.624661276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10671.625' to each side of the equation. -10671.625 + 10671.625 + x = -10669.624661276 + 10671.625 Combine like terms: -10671.625 + 10671.625 = 0.000 0.000 + x = -10669.624661276 + 10671.625 x = -10669.624661276 + 10671.625 Combine like terms: -10669.624661276 + 10671.625 = 2.000338724 x = 2.000338724 Simplifying x = 2.000338724

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21341.249661276, 2.000338724}

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