(x+4)(4x-2)=5(x+3)-10

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Solution for (x+4)(4x-2)=5(x+3)-10 equation: 


Simplifying
(x + 4)(4x + -2) = 5(x + 3) + -10

Reorder the terms:
(4 + x)(4x + -2) = 5(x + 3) + -10

Reorder the terms:
(4 + x)(-2 + 4x) = 5(x + 3) + -10

Multiply (4 + x) * (-2 + 4x)
(4(-2 + 4x) + x(-2 + 4x)) = 5(x + 3) + -10
((-2 * 4 + 4x * 4) + x(-2 + 4x)) = 5(x + 3) + -10
((-8 + 16x) + x(-2 + 4x)) = 5(x + 3) + -10
(-8 + 16x + (-2 * x + 4x * x)) = 5(x + 3) + -10
(-8 + 16x + (-2x + 4x2)) = 5(x + 3) + -10

Combine like terms: 16x + -2x = 14x
(-8 + 14x + 4x2) = 5(x + 3) + -10

Reorder the terms:
-8 + 14x + 4x2 = 5(3 + x) + -10
-8 + 14x + 4x2 = (3 * 5 + x * 5) + -10
-8 + 14x + 4x2 = (15 + 5x) + -10

Reorder the terms:
-8 + 14x + 4x2 = 15 + -10 + 5x

Combine like terms: 15 + -10 = 5
-8 + 14x + 4x2 = 5 + 5x

Solving
-8 + 14x + 4x2 = 5 + 5x

Solving for variable 'x'.

Reorder the terms:
-8 + -5 + 14x + -5x + 4x2 = 5 + 5x + -5 + -5x

Combine like terms: -8 + -5 = -13
-13 + 14x + -5x + 4x2 = 5 + 5x + -5 + -5x

Combine like terms: 14x + -5x = 9x
-13 + 9x + 4x2 = 5 + 5x + -5 + -5x

Reorder the terms:
-13 + 9x + 4x2 = 5 + -5 + 5x + -5x

Combine like terms: 5 + -5 = 0
-13 + 9x + 4x2 = 0 + 5x + -5x
-13 + 9x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-13 + 9x + 4x2 = 0

Factor a trinomial.
(-13 + -4x)(1 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-3.25, 1}

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