(7x+1)(7x+1)=(4-8x)(4-8x)

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Solution for (7x+1)(7x+1)=(4-8x)(4-8x) equation: 


Simplifying
(7x + 1)(7x + 1) = (4 + -8x)(4 + -8x)

Reorder the terms:
(1 + 7x)(7x + 1) = (4 + -8x)(4 + -8x)

Reorder the terms:
(1 + 7x)(1 + 7x) = (4 + -8x)(4 + -8x)

Multiply (1 + 7x) * (1 + 7x)
(1(1 + 7x) + 7x * (1 + 7x)) = (4 + -8x)(4 + -8x)
((1 * 1 + 7x * 1) + 7x * (1 + 7x)) = (4 + -8x)(4 + -8x)
((1 + 7x) + 7x * (1 + 7x)) = (4 + -8x)(4 + -8x)
(1 + 7x + (1 * 7x + 7x * 7x)) = (4 + -8x)(4 + -8x)
(1 + 7x + (7x + 49x2)) = (4 + -8x)(4 + -8x)

Combine like terms: 7x + 7x = 14x
(1 + 14x + 49x2) = (4 + -8x)(4 + -8x)

Multiply (4 + -8x) * (4 + -8x)
1 + 14x + 49x2 = (4(4 + -8x) + -8x * (4 + -8x))
1 + 14x + 49x2 = ((4 * 4 + -8x * 4) + -8x * (4 + -8x))
1 + 14x + 49x2 = ((16 + -32x) + -8x * (4 + -8x))
1 + 14x + 49x2 = (16 + -32x + (4 * -8x + -8x * -8x))
1 + 14x + 49x2 = (16 + -32x + (-32x + 64x2))

Combine like terms: -32x + -32x = -64x
1 + 14x + 49x2 = (16 + -64x + 64x2)

Solving
1 + 14x + 49x2 = 16 + -64x + 64x2

Solving for variable 'x'.

Reorder the terms:
1 + -16 + 14x + 64x + 49x2 + -64x2 = 16 + -64x + 64x2 + -16 + 64x + -64x2

Combine like terms: 1 + -16 = -15
-15 + 14x + 64x + 49x2 + -64x2 = 16 + -64x + 64x2 + -16 + 64x + -64x2

Combine like terms: 14x + 64x = 78x
-15 + 78x + 49x2 + -64x2 = 16 + -64x + 64x2 + -16 + 64x + -64x2

Combine like terms: 49x2 + -64x2 = -15x2
-15 + 78x + -15x2 = 16 + -64x + 64x2 + -16 + 64x + -64x2

Reorder the terms:
-15 + 78x + -15x2 = 16 + -16 + -64x + 64x + 64x2 + -64x2

Combine like terms: 16 + -16 = 0
-15 + 78x + -15x2 = 0 + -64x + 64x + 64x2 + -64x2
-15 + 78x + -15x2 = -64x + 64x + 64x2 + -64x2

Combine like terms: -64x + 64x = 0
-15 + 78x + -15x2 = 0 + 64x2 + -64x2
-15 + 78x + -15x2 = 64x2 + -64x2

Combine like terms: 64x2 + -64x2 = 0
-15 + 78x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 26x + -5x2) = 0

Factor a trinomial.
3((-5 + x)(1 + -5x)) = 0

Ignore the factor 3.

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

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

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

Simplifying
x = 5

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {5, 0.2}

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