(3x+7)(x-1)=24x

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Solution for (3x+7)(x-1)=24x equation: 


Simplifying
(3x + 7)(x + -1) = 24x

Reorder the terms:
(7 + 3x)(x + -1) = 24x

Reorder the terms:
(7 + 3x)(-1 + x) = 24x

Multiply (7 + 3x) * (-1 + x)
(7(-1 + x) + 3x * (-1 + x)) = 24x
((-1 * 7 + x * 7) + 3x * (-1 + x)) = 24x
((-7 + 7x) + 3x * (-1 + x)) = 24x
(-7 + 7x + (-1 * 3x + x * 3x)) = 24x
(-7 + 7x + (-3x + 3x2)) = 24x

Combine like terms: 7x + -3x = 4x
(-7 + 4x + 3x2) = 24x

Solving
-7 + 4x + 3x2 = 24x

Solving for variable 'x'.

Reorder the terms:
-7 + 4x + -24x + 3x2 = 24x + -24x

Combine like terms: 4x + -24x = -20x
-7 + -20x + 3x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-7 + -20x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(7 + -1x) = 0


Subproblem 1
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

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 = {-0.3333333333, 7}

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