(5x+8)(5x+8)=(4-7x)(4-7x)

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Solution for (5x+8)(5x+8)=(4-7x)(4-7x) equation: 


Simplifying
(5x + 8)(5x + 8) = (4 + -7x)(4 + -7x)

Reorder the terms:
(8 + 5x)(5x + 8) = (4 + -7x)(4 + -7x)

Reorder the terms:
(8 + 5x)(8 + 5x) = (4 + -7x)(4 + -7x)

Multiply (8 + 5x) * (8 + 5x)
(8(8 + 5x) + 5x * (8 + 5x)) = (4 + -7x)(4 + -7x)
((8 * 8 + 5x * 8) + 5x * (8 + 5x)) = (4 + -7x)(4 + -7x)
((64 + 40x) + 5x * (8 + 5x)) = (4 + -7x)(4 + -7x)
(64 + 40x + (8 * 5x + 5x * 5x)) = (4 + -7x)(4 + -7x)
(64 + 40x + (40x + 25x2)) = (4 + -7x)(4 + -7x)

Combine like terms: 40x + 40x = 80x
(64 + 80x + 25x2) = (4 + -7x)(4 + -7x)

Multiply (4 + -7x) * (4 + -7x)
64 + 80x + 25x2 = (4(4 + -7x) + -7x * (4 + -7x))
64 + 80x + 25x2 = ((4 * 4 + -7x * 4) + -7x * (4 + -7x))
64 + 80x + 25x2 = ((16 + -28x) + -7x * (4 + -7x))
64 + 80x + 25x2 = (16 + -28x + (4 * -7x + -7x * -7x))
64 + 80x + 25x2 = (16 + -28x + (-28x + 49x2))

Combine like terms: -28x + -28x = -56x
64 + 80x + 25x2 = (16 + -56x + 49x2)

Solving
64 + 80x + 25x2 = 16 + -56x + 49x2

Solving for variable 'x'.

Reorder the terms:
64 + -16 + 80x + 56x + 25x2 + -49x2 = 16 + -56x + 49x2 + -16 + 56x + -49x2

Combine like terms: 64 + -16 = 48
48 + 80x + 56x + 25x2 + -49x2 = 16 + -56x + 49x2 + -16 + 56x + -49x2

Combine like terms: 80x + 56x = 136x
48 + 136x + 25x2 + -49x2 = 16 + -56x + 49x2 + -16 + 56x + -49x2

Combine like terms: 25x2 + -49x2 = -24x2
48 + 136x + -24x2 = 16 + -56x + 49x2 + -16 + 56x + -49x2

Reorder the terms:
48 + 136x + -24x2 = 16 + -16 + -56x + 56x + 49x2 + -49x2

Combine like terms: 16 + -16 = 0
48 + 136x + -24x2 = 0 + -56x + 56x + 49x2 + -49x2
48 + 136x + -24x2 = -56x + 56x + 49x2 + -49x2

Combine like terms: -56x + 56x = 0
48 + 136x + -24x2 = 0 + 49x2 + -49x2
48 + 136x + -24x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
48 + 136x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + 17x + -3x2) = 0

Factor a trinomial.
8((6 + -1x)(1 + 3x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
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
Solution
x = {6, -0.3333333333}

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