7x(1+3x)+(3x+1)(x-8)=0

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Solution for 7x(1+3x)+(3x+1)(x-8)=0 equation: 


Simplifying
7x(1 + 3x) + (3x + 1)(x + -8) = 0
(1 * 7x + 3x * 7x) + (3x + 1)(x + -8) = 0
(7x + 21x2) + (3x + 1)(x + -8) = 0

Reorder the terms:
7x + 21x2 + (1 + 3x)(x + -8) = 0

Reorder the terms:
7x + 21x2 + (1 + 3x)(-8 + x) = 0

Multiply (1 + 3x) * (-8 + x)
7x + 21x2 + (1(-8 + x) + 3x * (-8 + x)) = 0
7x + 21x2 + ((-8 * 1 + x * 1) + 3x * (-8 + x)) = 0
7x + 21x2 + ((-8 + 1x) + 3x * (-8 + x)) = 0
7x + 21x2 + (-8 + 1x + (-8 * 3x + x * 3x)) = 0
7x + 21x2 + (-8 + 1x + (-24x + 3x2)) = 0

Combine like terms: 1x + -24x = -23x
7x + 21x2 + (-8 + -23x + 3x2) = 0

Reorder the terms:
-8 + 7x + -23x + 21x2 + 3x2 = 0

Combine like terms: 7x + -23x = -16x
-8 + -16x + 21x2 + 3x2 = 0

Combine like terms: 21x2 + 3x2 = 24x2
-8 + -16x + 24x2 = 0

Solving
-8 + -16x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + -2x + 3x2) = 0

Factor a trinomial.
8((-1 + -3x)(1 + -1x)) = 0

Ignore the factor 8.

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

Simplifying
-1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.3333333333, 1}

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