(8-3x)(8-3x)+(x-5)(8-3x)=0

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Solution for (8-3x)(8-3x)+(x-5)(8-3x)=0 equation: 


Simplifying
(8 + -3x)(8 + -3x) + (x + -5)(8 + -3x) = 0

Multiply (8 + -3x) * (8 + -3x)
(8(8 + -3x) + -3x * (8 + -3x)) + (x + -5)(8 + -3x) = 0
((8 * 8 + -3x * 8) + -3x * (8 + -3x)) + (x + -5)(8 + -3x) = 0
((64 + -24x) + -3x * (8 + -3x)) + (x + -5)(8 + -3x) = 0
(64 + -24x + (8 * -3x + -3x * -3x)) + (x + -5)(8 + -3x) = 0
(64 + -24x + (-24x + 9x2)) + (x + -5)(8 + -3x) = 0

Combine like terms: -24x + -24x = -48x
(64 + -48x + 9x2) + (x + -5)(8 + -3x) = 0

Reorder the terms:
64 + -48x + 9x2 + (-5 + x)(8 + -3x) = 0

Multiply (-5 + x) * (8 + -3x)
64 + -48x + 9x2 + (-5(8 + -3x) + x(8 + -3x)) = 0
64 + -48x + 9x2 + ((8 * -5 + -3x * -5) + x(8 + -3x)) = 0
64 + -48x + 9x2 + ((-40 + 15x) + x(8 + -3x)) = 0
64 + -48x + 9x2 + (-40 + 15x + (8 * x + -3x * x)) = 0
64 + -48x + 9x2 + (-40 + 15x + (8x + -3x2)) = 0

Combine like terms: 15x + 8x = 23x
64 + -48x + 9x2 + (-40 + 23x + -3x2) = 0

Reorder the terms:
64 + -40 + -48x + 23x + 9x2 + -3x2 = 0

Combine like terms: 64 + -40 = 24
24 + -48x + 23x + 9x2 + -3x2 = 0

Combine like terms: -48x + 23x = -25x
24 + -25x + 9x2 + -3x2 = 0

Combine like terms: 9x2 + -3x2 = 6x2
24 + -25x + 6x2 = 0

Solving
24 + -25x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(8 + -3x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {1.5, 2.666666667}

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