(1+2x)*(1+2x)-7x=3x*3x-1

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


Simplifying
(1 + 2x)(1 + 2x) + -7x = 3x * 3x + -1

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

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

Reorder the terms:
1 + 4x + -7x + 4x2 = 3x * 3x + -1

Combine like terms: 4x + -7x = -3x
1 + -3x + 4x2 = 3x * 3x + -1

Reorder the terms for easier multiplication:
1 + -3x + 4x2 = 3 * 3x * x + -1

Multiply 3 * 3
1 + -3x + 4x2 = 9x * x + -1

Multiply x * x
1 + -3x + 4x2 = 9x2 + -1

Reorder the terms:
1 + -3x + 4x2 = -1 + 9x2

Solving
1 + -3x + 4x2 = -1 + 9x2

Solving for variable 'x'.

Reorder the terms:
1 + 1 + -3x + 4x2 + -9x2 = -1 + 9x2 + 1 + -9x2

Combine like terms: 1 + 1 = 2
2 + -3x + 4x2 + -9x2 = -1 + 9x2 + 1 + -9x2

Combine like terms: 4x2 + -9x2 = -5x2
2 + -3x + -5x2 = -1 + 9x2 + 1 + -9x2

Reorder the terms:
2 + -3x + -5x2 = -1 + 1 + 9x2 + -9x2

Combine like terms: -1 + 1 = 0
2 + -3x + -5x2 = 0 + 9x2 + -9x2
2 + -3x + -5x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
2 + -3x + -5x2 = 0

Factor a trinomial.
(2 + -5x)(1 + x) = 0


Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0.4, -1}

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