(4x-10)(x+1)=3(x+4)-9

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Solution for (4x-10)(x+1)=3(x+4)-9 equation: 


Simplifying
(4x + -10)(x + 1) = 3(x + 4) + -9

Reorder the terms:
(-10 + 4x)(x + 1) = 3(x + 4) + -9

Reorder the terms:
(-10 + 4x)(1 + x) = 3(x + 4) + -9

Multiply (-10 + 4x) * (1 + x)
(-10(1 + x) + 4x * (1 + x)) = 3(x + 4) + -9
((1 * -10 + x * -10) + 4x * (1 + x)) = 3(x + 4) + -9
((-10 + -10x) + 4x * (1 + x)) = 3(x + 4) + -9
(-10 + -10x + (1 * 4x + x * 4x)) = 3(x + 4) + -9
(-10 + -10x + (4x + 4x2)) = 3(x + 4) + -9

Combine like terms: -10x + 4x = -6x
(-10 + -6x + 4x2) = 3(x + 4) + -9

Reorder the terms:
-10 + -6x + 4x2 = 3(4 + x) + -9
-10 + -6x + 4x2 = (4 * 3 + x * 3) + -9
-10 + -6x + 4x2 = (12 + 3x) + -9

Reorder the terms:
-10 + -6x + 4x2 = 12 + -9 + 3x

Combine like terms: 12 + -9 = 3
-10 + -6x + 4x2 = 3 + 3x

Solving
-10 + -6x + 4x2 = 3 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + -3 + -6x + -3x + 4x2 = 3 + 3x + -3 + -3x

Combine like terms: -10 + -3 = -13
-13 + -6x + -3x + 4x2 = 3 + 3x + -3 + -3x

Combine like terms: -6x + -3x = -9x
-13 + -9x + 4x2 = 3 + 3x + -3 + -3x

Reorder the terms:
-13 + -9x + 4x2 = 3 + -3 + 3x + -3x

Combine like terms: 3 + -3 = 0
-13 + -9x + 4x2 = 0 + 3x + -3x
-13 + -9x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-13 + -9x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(13 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 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 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {-1, 3.25}

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