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

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


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

Reorder the terms:
3x(-4 + x) + 2(2x + -4) = 2x + 5
(-4 * 3x + x * 3x) + 2(2x + -4) = 2x + 5
(-12x + 3x2) + 2(2x + -4) = 2x + 5

Reorder the terms:
-12x + 3x2 + 2(-4 + 2x) = 2x + 5
-12x + 3x2 + (-4 * 2 + 2x * 2) = 2x + 5
-12x + 3x2 + (-8 + 4x) = 2x + 5

Reorder the terms:
-8 + -12x + 4x + 3x2 = 2x + 5

Combine like terms: -12x + 4x = -8x
-8 + -8x + 3x2 = 2x + 5

Reorder the terms:
-8 + -8x + 3x2 = 5 + 2x

Solving
-8 + -8x + 3x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + -5 + -8x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: -8 + -5 = -13
-13 + -8x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: -8x + -2x = -10x
-13 + -10x + 3x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-13 + -10x + 3x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-13 + -10x + 3x2 = 0 + 2x + -2x
-13 + -10x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-13 + -10x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(13 + -3x) = 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 '(13 + -3x)' equal to zero and attempt to solve:

Simplifying
13 + -3x = 0

Solving
13 + -3x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -3x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3x = 0 + -13
-3x = 0 + -13

Combine like terms: 0 + -13 = -13
-3x = -13

Divide each side by '-3'.
x = 4.333333333

Simplifying
x = 4.333333333
Solution
x = {-1, 4.333333333}

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