(4x-1)(x-5)=10x+95

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Solution for (4x-1)(x-5)=10x+95 equation: 


Simplifying
(4x + -1)(x + -5) = 10x + 95

Reorder the terms:
(-1 + 4x)(x + -5) = 10x + 95

Reorder the terms:
(-1 + 4x)(-5 + x) = 10x + 95

Multiply (-1 + 4x) * (-5 + x)
(-1(-5 + x) + 4x * (-5 + x)) = 10x + 95
((-5 * -1 + x * -1) + 4x * (-5 + x)) = 10x + 95
((5 + -1x) + 4x * (-5 + x)) = 10x + 95
(5 + -1x + (-5 * 4x + x * 4x)) = 10x + 95
(5 + -1x + (-20x + 4x2)) = 10x + 95

Combine like terms: -1x + -20x = -21x
(5 + -21x + 4x2) = 10x + 95

Reorder the terms:
5 + -21x + 4x2 = 95 + 10x

Solving
5 + -21x + 4x2 = 95 + 10x

Solving for variable 'x'.

Reorder the terms:
5 + -95 + -21x + -10x + 4x2 = 95 + 10x + -95 + -10x

Combine like terms: 5 + -95 = -90
-90 + -21x + -10x + 4x2 = 95 + 10x + -95 + -10x

Combine like terms: -21x + -10x = -31x
-90 + -31x + 4x2 = 95 + 10x + -95 + -10x

Reorder the terms:
-90 + -31x + 4x2 = 95 + -95 + 10x + -10x

Combine like terms: 95 + -95 = 0
-90 + -31x + 4x2 = 0 + 10x + -10x
-90 + -31x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-90 + -31x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-2.25, 10}

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