(4x-1)(x+7)+5(x+7)=

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Solution for (4x-1)(x+7)+5(x+7)= equation:


Simplifying
(4x + -1)(x + 7) + 5(x + 7) = 0

Reorder the terms:
(-1 + 4x)(x + 7) + 5(x + 7) = 0

Reorder the terms:
(-1 + 4x)(7 + x) + 5(x + 7) = 0

Multiply (-1 + 4x) * (7 + x)
(-1(7 + x) + 4x * (7 + x)) + 5(x + 7) = 0
((7 * -1 + x * -1) + 4x * (7 + x)) + 5(x + 7) = 0
((-7 + -1x) + 4x * (7 + x)) + 5(x + 7) = 0
(-7 + -1x + (7 * 4x + x * 4x)) + 5(x + 7) = 0
(-7 + -1x + (28x + 4x2)) + 5(x + 7) = 0

Combine like terms: -1x + 28x = 27x
(-7 + 27x + 4x2) + 5(x + 7) = 0

Reorder the terms:
-7 + 27x + 4x2 + 5(7 + x) = 0
-7 + 27x + 4x2 + (7 * 5 + x * 5) = 0
-7 + 27x + 4x2 + (35 + 5x) = 0

Reorder the terms:
-7 + 35 + 27x + 5x + 4x2 = 0

Combine like terms: -7 + 35 = 28
28 + 27x + 5x + 4x2 = 0

Combine like terms: 27x + 5x = 32x
28 + 32x + 4x2 = 0

Solving
28 + 32x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 8x + x2) = 0

Factor a trinomial.
4((7 + x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-7, -1}

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