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

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


Simplifying
(1 + -3x)(1 + 3x) = 7x + 1

Multiply (1 + -3x) * (1 + 3x)
(1(1 + 3x) + -3x * (1 + 3x)) = 7x + 1
((1 * 1 + 3x * 1) + -3x * (1 + 3x)) = 7x + 1
((1 + 3x) + -3x * (1 + 3x)) = 7x + 1
(1 + 3x + (1 * -3x + 3x * -3x)) = 7x + 1
(1 + 3x + (-3x + -9x2)) = 7x + 1

Combine like terms: 3x + -3x = 0
(1 + 0 + -9x2) = 7x + 1
(1 + -9x2) = 7x + 1

Reorder the terms:
1 + -9x2 = 1 + 7x

Add '-1' to each side of the equation.
1 + -1 + -9x2 = 1 + -1 + 7x

Combine like terms: 1 + -1 = 0
0 + -9x2 = 1 + -1 + 7x
-9x2 = 1 + -1 + 7x

Combine like terms: 1 + -1 = 0
-9x2 = 0 + 7x
-9x2 = 7x

Solving
-9x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-7x + -9x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-7x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(7 + 9x) = 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 '(7 + 9x)' equal to zero and attempt to solve:

Simplifying
7 + 9x = 0

Solving
7 + 9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9x = 0 + -7
9x = 0 + -7

Combine like terms: 0 + -7 = -7
9x = -7

Divide each side by '9'.
x = -0.7777777778

Simplifying
x = -0.7777777778
Solution
x = {0, -0.7777777778}

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