2(3x-21)+x-7=(3x-21)(8x-56)

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Solution for 2(3x-21)+x-7=(3x-21)(8x-56) equation: 


Simplifying
2(3x + -21) + x + -7 = (3x + -21)(8x + -56)

Reorder the terms:
2(-21 + 3x) + x + -7 = (3x + -21)(8x + -56)
(-21 * 2 + 3x * 2) + x + -7 = (3x + -21)(8x + -56)
(-42 + 6x) + x + -7 = (3x + -21)(8x + -56)

Reorder the terms:
-42 + -7 + 6x + x = (3x + -21)(8x + -56)

Combine like terms: -42 + -7 = -49
-49 + 6x + x = (3x + -21)(8x + -56)

Combine like terms: 6x + x = 7x
-49 + 7x = (3x + -21)(8x + -56)

Reorder the terms:
-49 + 7x = (-21 + 3x)(8x + -56)

Reorder the terms:
-49 + 7x = (-21 + 3x)(-56 + 8x)

Multiply (-21 + 3x) * (-56 + 8x)
-49 + 7x = (-21(-56 + 8x) + 3x * (-56 + 8x))
-49 + 7x = ((-56 * -21 + 8x * -21) + 3x * (-56 + 8x))
-49 + 7x = ((1176 + -168x) + 3x * (-56 + 8x))
-49 + 7x = (1176 + -168x + (-56 * 3x + 8x * 3x))
-49 + 7x = (1176 + -168x + (-168x + 24x2))

Combine like terms: -168x + -168x = -336x
-49 + 7x = (1176 + -336x + 24x2)

Solving
-49 + 7x = 1176 + -336x + 24x2

Solving for variable 'x'.

Reorder the terms:
-49 + -1176 + 7x + 336x + -24x2 = 1176 + -336x + 24x2 + -1176 + 336x + -24x2

Combine like terms: -49 + -1176 = -1225
-1225 + 7x + 336x + -24x2 = 1176 + -336x + 24x2 + -1176 + 336x + -24x2

Combine like terms: 7x + 336x = 343x
-1225 + 343x + -24x2 = 1176 + -336x + 24x2 + -1176 + 336x + -24x2

Reorder the terms:
-1225 + 343x + -24x2 = 1176 + -1176 + -336x + 336x + 24x2 + -24x2

Combine like terms: 1176 + -1176 = 0
-1225 + 343x + -24x2 = 0 + -336x + 336x + 24x2 + -24x2
-1225 + 343x + -24x2 = -336x + 336x + 24x2 + -24x2

Combine like terms: -336x + 336x = 0
-1225 + 343x + -24x2 = 0 + 24x2 + -24x2
-1225 + 343x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-1225 + 343x + -24x2 = 0

Factor a trinomial.
(-175 + 24x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-175 + 24x)' equal to zero and attempt to solve:

Simplifying
-175 + 24x = 0

Solving
-175 + 24x = 0

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

Add '175' to each side of the equation.
-175 + 175 + 24x = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 24x = 0 + 175
24x = 0 + 175

Combine like terms: 0 + 175 = 175
24x = 175

Divide each side by '24'.
x = 7.291666667

Simplifying
x = 7.291666667

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {7.291666667, 7}

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