5x(x-3)-8=4x(x-2)

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Solution for 5x(x-3)-8=4x(x-2) equation: 


Simplifying
5x(x + -3) + -8 = 4x(x + -2)

Reorder the terms:
5x(-3 + x) + -8 = 4x(x + -2)
(-3 * 5x + x * 5x) + -8 = 4x(x + -2)
(-15x + 5x2) + -8 = 4x(x + -2)

Reorder the terms:
-8 + -15x + 5x2 = 4x(x + -2)

Reorder the terms:
-8 + -15x + 5x2 = 4x(-2 + x)
-8 + -15x + 5x2 = (-2 * 4x + x * 4x)
-8 + -15x + 5x2 = (-8x + 4x2)

Solving
-8 + -15x + 5x2 = -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
-8 + -15x + 8x + 5x2 + -4x2 = -8x + 4x2 + 8x + -4x2

Combine like terms: -15x + 8x = -7x
-8 + -7x + 5x2 + -4x2 = -8x + 4x2 + 8x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-8 + -7x + 1x2 = -8x + 4x2 + 8x + -4x2

Reorder the terms:
-8 + -7x + 1x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
-8 + -7x + 1x2 = 0 + 4x2 + -4x2
-8 + -7x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + -7x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -1x) = 0


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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1, 8}

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