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

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


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

Reorder the terms:
8x(-3 + x) = (2x + 7)(x + -3)
(-3 * 8x + x * 8x) = (2x + 7)(x + -3)
(-24x + 8x2) = (2x + 7)(x + -3)

Reorder the terms:
-24x + 8x2 = (7 + 2x)(x + -3)

Reorder the terms:
-24x + 8x2 = (7 + 2x)(-3 + x)

Multiply (7 + 2x) * (-3 + x)
-24x + 8x2 = (7(-3 + x) + 2x * (-3 + x))
-24x + 8x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x))
-24x + 8x2 = ((-21 + 7x) + 2x * (-3 + x))
-24x + 8x2 = (-21 + 7x + (-3 * 2x + x * 2x))
-24x + 8x2 = (-21 + 7x + (-6x + 2x2))

Combine like terms: 7x + -6x = 1x
-24x + 8x2 = (-21 + 1x + 2x2)

Solving
-24x + 8x2 = -21 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
21 + -24x + -1x + 8x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: -24x + -1x = -25x
21 + -25x + 8x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
21 + -25x + 6x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Reorder the terms:
21 + -25x + 6x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
21 + -25x + 6x2 = 0 + 1x + -1x + 2x2 + -2x2
21 + -25x + 6x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
21 + -25x + 6x2 = 0 + 2x2 + -2x2
21 + -25x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
21 + -25x + 6x2 = 0

Factor a trinomial.
(7 + -6x)(3 + -1x) = 0


Subproblem 1
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.166666667, 3}

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