(x+4)(4x+1)=-11

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Solution for (x+4)(4x+1)=-11 equation:


Simplifying
(x + 4)(4x + 1) = -11

Reorder the terms:
(4 + x)(4x + 1) = -11

Reorder the terms:
(4 + x)(1 + 4x) = -11

Multiply (4 + x) * (1 + 4x)
(4(1 + 4x) + x(1 + 4x)) = -11
((1 * 4 + 4x * 4) + x(1 + 4x)) = -11
((4 + 16x) + x(1 + 4x)) = -11
(4 + 16x + (1 * x + 4x * x)) = -11
(4 + 16x + (1x + 4x2)) = -11

Combine like terms: 16x + 1x = 17x
(4 + 17x + 4x2) = -11

Solving
4 + 17x + 4x2 = -11

Solving for variable 'x'.

Reorder the terms:
4 + 11 + 17x + 4x2 = -11 + 11

Combine like terms: 4 + 11 = 15
15 + 17x + 4x2 = -11 + 11

Combine like terms: -11 + 11 = 0
15 + 17x + 4x2 = 0

Factor a trinomial.
(3 + x)(5 + 4x) = 0

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25

Solution

x = {-3, -1.25}

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