(5x-6)*(5x-6)=(3x+1)*(3x+1)

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Solution for (5x-6)*(5x-6)=(3x+1)*(3x+1) equation: 


Simplifying
(5x + -6)(5x + -6) = (3x + 1)(3x + 1)

Reorder the terms:
(-6 + 5x)(5x + -6) = (3x + 1)(3x + 1)

Reorder the terms:
(-6 + 5x)(-6 + 5x) = (3x + 1)(3x + 1)

Multiply (-6 + 5x) * (-6 + 5x)
(-6(-6 + 5x) + 5x * (-6 + 5x)) = (3x + 1)(3x + 1)
((-6 * -6 + 5x * -6) + 5x * (-6 + 5x)) = (3x + 1)(3x + 1)
((36 + -30x) + 5x * (-6 + 5x)) = (3x + 1)(3x + 1)
(36 + -30x + (-6 * 5x + 5x * 5x)) = (3x + 1)(3x + 1)
(36 + -30x + (-30x + 25x2)) = (3x + 1)(3x + 1)

Combine like terms: -30x + -30x = -60x
(36 + -60x + 25x2) = (3x + 1)(3x + 1)

Reorder the terms:
36 + -60x + 25x2 = (1 + 3x)(3x + 1)

Reorder the terms:
36 + -60x + 25x2 = (1 + 3x)(1 + 3x)

Multiply (1 + 3x) * (1 + 3x)
36 + -60x + 25x2 = (1(1 + 3x) + 3x * (1 + 3x))
36 + -60x + 25x2 = ((1 * 1 + 3x * 1) + 3x * (1 + 3x))
36 + -60x + 25x2 = ((1 + 3x) + 3x * (1 + 3x))
36 + -60x + 25x2 = (1 + 3x + (1 * 3x + 3x * 3x))
36 + -60x + 25x2 = (1 + 3x + (3x + 9x2))

Combine like terms: 3x + 3x = 6x
36 + -60x + 25x2 = (1 + 6x + 9x2)

Solving
36 + -60x + 25x2 = 1 + 6x + 9x2

Solving for variable 'x'.

Reorder the terms:
36 + -1 + -60x + -6x + 25x2 + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Combine like terms: 36 + -1 = 35
35 + -60x + -6x + 25x2 + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Combine like terms: -60x + -6x = -66x
35 + -66x + 25x2 + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Combine like terms: 25x2 + -9x2 = 16x2
35 + -66x + 16x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2

Reorder the terms:
35 + -66x + 16x2 = 1 + -1 + 6x + -6x + 9x2 + -9x2

Combine like terms: 1 + -1 = 0
35 + -66x + 16x2 = 0 + 6x + -6x + 9x2 + -9x2
35 + -66x + 16x2 = 6x + -6x + 9x2 + -9x2

Combine like terms: 6x + -6x = 0
35 + -66x + 16x2 = 0 + 9x2 + -9x2
35 + -66x + 16x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
35 + -66x + 16x2 = 0

Factor a trinomial.
(5 + -8x)(7 + -2x) = 0


Subproblem 1
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 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 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.625, 3.5}

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