(4X+7)(X+1)=10

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Solution for (4X+7)(X+1)=10 equation: 


Simplifying
(4X + 7)(X + 1) = 10

Reorder the terms:
(7 + 4X)(X + 1) = 10

Reorder the terms:
(7 + 4X)(1 + X) = 10

Multiply (7 + 4X) * (1 + X)
(7(1 + X) + 4X * (1 + X)) = 10
((1 * 7 + X * 7) + 4X * (1 + X)) = 10
((7 + 7X) + 4X * (1 + X)) = 10
(7 + 7X + (1 * 4X + X * 4X)) = 10
(7 + 7X + (4X + 4X2)) = 10

Combine like terms: 7X + 4X = 11X
(7 + 11X + 4X2) = 10

Solving
7 + 11X + 4X2 = 10

Solving for variable 'X'.

Reorder the terms:
7 + -10 + 11X + 4X2 = 10 + -10

Combine like terms: 7 + -10 = -3
-3 + 11X + 4X2 = 10 + -10

Combine like terms: 10 + -10 = 0
-3 + 11X + 4X2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -4X)' equal to zero and attempt to solve:

Simplifying
1 + -4X = 0

Solving
1 + -4X = 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 + -4X = 0 + -1

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

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

Divide each side by '-4'.
X = 0.25

Simplifying
X = 0.25
Solution
X = {-3, 0.25}

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