3(x+10)(8-3x)=4(8-3x)

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Solution for 3(x+10)(8-3x)=4(8-3x) equation: 


Simplifying
3(x + 10)(8 + -3x) = 4(8 + -3x)

Reorder the terms:
3(10 + x)(8 + -3x) = 4(8 + -3x)

Multiply (10 + x) * (8 + -3x)
3(10(8 + -3x) + x(8 + -3x)) = 4(8 + -3x)
3((8 * 10 + -3x * 10) + x(8 + -3x)) = 4(8 + -3x)
3((80 + -30x) + x(8 + -3x)) = 4(8 + -3x)
3(80 + -30x + (8 * x + -3x * x)) = 4(8 + -3x)
3(80 + -30x + (8x + -3x2)) = 4(8 + -3x)

Combine like terms: -30x + 8x = -22x
3(80 + -22x + -3x2) = 4(8 + -3x)
(80 * 3 + -22x * 3 + -3x2 * 3) = 4(8 + -3x)
(240 + -66x + -9x2) = 4(8 + -3x)
240 + -66x + -9x2 = (8 * 4 + -3x * 4)
240 + -66x + -9x2 = (32 + -12x)

Solving
240 + -66x + -9x2 = 32 + -12x

Solving for variable 'x'.

Reorder the terms:
240 + -32 + -66x + 12x + -9x2 = 32 + -12x + -32 + 12x

Combine like terms: 240 + -32 = 208
208 + -66x + 12x + -9x2 = 32 + -12x + -32 + 12x

Combine like terms: -66x + 12x = -54x
208 + -54x + -9x2 = 32 + -12x + -32 + 12x

Reorder the terms:
208 + -54x + -9x2 = 32 + -32 + -12x + 12x

Combine like terms: 32 + -32 = 0
208 + -54x + -9x2 = 0 + -12x + 12x
208 + -54x + -9x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
208 + -54x + -9x2 = 0

Factor a trinomial.
(8 + -3x)(26 + 3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(26 + 3x)' equal to zero and attempt to solve:

Simplifying
26 + 3x = 0

Solving
26 + 3x = 0

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

Add '-26' to each side of the equation.
26 + -26 + 3x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 3x = 0 + -26
3x = 0 + -26

Combine like terms: 0 + -26 = -26
3x = -26

Divide each side by '3'.
x = -8.666666667

Simplifying
x = -8.666666667
Solution
x = {2.666666667, -8.666666667}

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