(4x-1)(x-3)=15

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Solution for (4x-1)(x-3)=15 equation: 


Simplifying
(4x + -1)(x + -3) = 15

Reorder the terms:
(-1 + 4x)(x + -3) = 15

Reorder the terms:
(-1 + 4x)(-3 + x) = 15

Multiply (-1 + 4x) * (-3 + x)
(-1(-3 + x) + 4x * (-3 + x)) = 15
((-3 * -1 + x * -1) + 4x * (-3 + x)) = 15
((3 + -1x) + 4x * (-3 + x)) = 15
(3 + -1x + (-3 * 4x + x * 4x)) = 15
(3 + -1x + (-12x + 4x2)) = 15

Combine like terms: -1x + -12x = -13x
(3 + -13x + 4x2) = 15

Solving
3 + -13x + 4x2 = 15

Solving for variable 'x'.

Reorder the terms:
3 + -15 + -13x + 4x2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + -13x + 4x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + -13x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
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
Solution
x = {-0.75, 4}

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