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

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


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

Reorder the terms:
(-4 + 3x)(x + -4) = -5

Reorder the terms:
(-4 + 3x)(-4 + x) = -5

Multiply (-4 + 3x) * (-4 + x)
(-4(-4 + x) + 3x * (-4 + x)) = -5
((-4 * -4 + x * -4) + 3x * (-4 + x)) = -5
((16 + -4x) + 3x * (-4 + x)) = -5
(16 + -4x + (-4 * 3x + x * 3x)) = -5
(16 + -4x + (-12x + 3x2)) = -5

Combine like terms: -4x + -12x = -16x
(16 + -16x + 3x2) = -5

Solving
16 + -16x + 3x2 = -5

Solving for variable 'x'.

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

Combine like terms: 16 + 5 = 21
21 + -16x + 3x2 = -5 + 5

Combine like terms: -5 + 5 = 0
21 + -16x + 3x2 = 0

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


Subproblem 1
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

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 = {2.333333333, 3}

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