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

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


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

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

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

Remove parenthesis around (7 + 2x)
-24x + 8x2 = 7 + 2x

Solving
-24x + 8x2 = 7 + 2x

Solving for variable 'x'.

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

Combine like terms: -24x + -2x = -26x
-7 + -26x + 8x2 = 7 + 2x + -7 + -2x

Reorder the terms:
-7 + -26x + 8x2 = 7 + -7 + 2x + -2x

Combine like terms: 7 + -7 = 0
-7 + -26x + 8x2 = 0 + 2x + -2x
-7 + -26x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-7 + -26x + 8x2 = 0

Factor a trinomial.
(-1 + -4x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-0.25, 3.5}

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