7x(x-3)-(2x+1)(4x-1)=3x^2+1

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Solution for 7x(x-3)-(2x+1)(4x-1)=3x^2+1 equation: 


Simplifying
7x(x + -3) + -1(2x + 1)(4x + -1) = 3x2 + 1

Reorder the terms:
7x(-3 + x) + -1(2x + 1)(4x + -1) = 3x2 + 1
(-3 * 7x + x * 7x) + -1(2x + 1)(4x + -1) = 3x2 + 1
(-21x + 7x2) + -1(2x + 1)(4x + -1) = 3x2 + 1

Reorder the terms:
-21x + 7x2 + -1(1 + 2x)(4x + -1) = 3x2 + 1

Reorder the terms:
-21x + 7x2 + -1(1 + 2x)(-1 + 4x) = 3x2 + 1

Multiply (1 + 2x) * (-1 + 4x)
-21x + 7x2 + -1(1(-1 + 4x) + 2x * (-1 + 4x)) = 3x2 + 1
-21x + 7x2 + -1((-1 * 1 + 4x * 1) + 2x * (-1 + 4x)) = 3x2 + 1
-21x + 7x2 + -1((-1 + 4x) + 2x * (-1 + 4x)) = 3x2 + 1
-21x + 7x2 + -1(-1 + 4x + (-1 * 2x + 4x * 2x)) = 3x2 + 1
-21x + 7x2 + -1(-1 + 4x + (-2x + 8x2)) = 3x2 + 1

Combine like terms: 4x + -2x = 2x
-21x + 7x2 + -1(-1 + 2x + 8x2) = 3x2 + 1
-21x + 7x2 + (-1 * -1 + 2x * -1 + 8x2 * -1) = 3x2 + 1
-21x + 7x2 + (1 + -2x + -8x2) = 3x2 + 1

Reorder the terms:
1 + -21x + -2x + 7x2 + -8x2 = 3x2 + 1

Combine like terms: -21x + -2x = -23x
1 + -23x + 7x2 + -8x2 = 3x2 + 1

Combine like terms: 7x2 + -8x2 = -1x2
1 + -23x + -1x2 = 3x2 + 1

Reorder the terms:
1 + -23x + -1x2 = 1 + 3x2

Add '-1' to each side of the equation.
1 + -23x + -1 + -1x2 = 1 + -1 + 3x2

Reorder the terms:
1 + -1 + -23x + -1x2 = 1 + -1 + 3x2

Combine like terms: 1 + -1 = 0
0 + -23x + -1x2 = 1 + -1 + 3x2
-23x + -1x2 = 1 + -1 + 3x2

Combine like terms: 1 + -1 = 0
-23x + -1x2 = 0 + 3x2
-23x + -1x2 = 3x2

Solving
-23x + -1x2 = 3x2

Solving for variable 'x'.

Combine like terms: -1x2 + -3x2 = -4x2
-23x + -4x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-23x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(23 + 4x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(23 + 4x)' equal to zero and attempt to solve:

Simplifying
23 + 4x = 0

Solving
23 + 4x = 0

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

Add '-23' to each side of the equation.
23 + -23 + 4x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 4x = 0 + -23
4x = 0 + -23

Combine like terms: 0 + -23 = -23
4x = -23

Divide each side by '4'.
x = -5.75

Simplifying
x = -5.75
Solution
x = {0, -5.75}

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