x(8x+3)=3x^2-13x+16

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Solution for x(8x+3)=3x^2-13x+16 equation: 


Simplifying
x(8x + 3) = 3x2 + -13x + 16

Reorder the terms:
x(3 + 8x) = 3x2 + -13x + 16
(3 * x + 8x * x) = 3x2 + -13x + 16
(3x + 8x2) = 3x2 + -13x + 16

Reorder the terms:
3x + 8x2 = 16 + -13x + 3x2

Solving
3x + 8x2 = 16 + -13x + 3x2

Solving for variable 'x'.

Reorder the terms:
-16 + 3x + 13x + 8x2 + -3x2 = 16 + -13x + 3x2 + -16 + 13x + -3x2

Combine like terms: 3x + 13x = 16x
-16 + 16x + 8x2 + -3x2 = 16 + -13x + 3x2 + -16 + 13x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-16 + 16x + 5x2 = 16 + -13x + 3x2 + -16 + 13x + -3x2

Reorder the terms:
-16 + 16x + 5x2 = 16 + -16 + -13x + 13x + 3x2 + -3x2

Combine like terms: 16 + -16 = 0
-16 + 16x + 5x2 = 0 + -13x + 13x + 3x2 + -3x2
-16 + 16x + 5x2 = -13x + 13x + 3x2 + -3x2

Combine like terms: -13x + 13x = 0
-16 + 16x + 5x2 = 0 + 3x2 + -3x2
-16 + 16x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-16 + 16x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(4 + -5x) = 0


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-4, 0.8}

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