(2x+1)(x+4)-(x+4)(3-5x)=0

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Solution for (2x+1)(x+4)-(x+4)(3-5x)=0 equation:


Simplifying
(2x + 1)(x + 4) + -1(x + 4)(3 + -5x) = 0

Reorder the terms:
(1 + 2x)(x + 4) + -1(x + 4)(3 + -5x) = 0

Reorder the terms:
(1 + 2x)(4 + x) + -1(x + 4)(3 + -5x) = 0

Multiply (1 + 2x) * (4 + x)
(1(4 + x) + 2x * (4 + x)) + -1(x + 4)(3 + -5x) = 0
((4 * 1 + x * 1) + 2x * (4 + x)) + -1(x + 4)(3 + -5x) = 0
((4 + 1x) + 2x * (4 + x)) + -1(x + 4)(3 + -5x) = 0
(4 + 1x + (4 * 2x + x * 2x)) + -1(x + 4)(3 + -5x) = 0
(4 + 1x + (8x + 2x2)) + -1(x + 4)(3 + -5x) = 0

Combine like terms: 1x + 8x = 9x
(4 + 9x + 2x2) + -1(x + 4)(3 + -5x) = 0

Reorder the terms:
4 + 9x + 2x2 + -1(4 + x)(3 + -5x) = 0

Multiply (4 + x) * (3 + -5x)
4 + 9x + 2x2 + -1(4(3 + -5x) + x(3 + -5x)) = 0
4 + 9x + 2x2 + -1((3 * 4 + -5x * 4) + x(3 + -5x)) = 0
4 + 9x + 2x2 + -1((12 + -20x) + x(3 + -5x)) = 0
4 + 9x + 2x2 + -1(12 + -20x + (3 * x + -5x * x)) = 0
4 + 9x + 2x2 + -1(12 + -20x + (3x + -5x2)) = 0

Combine like terms: -20x + 3x = -17x
4 + 9x + 2x2 + -1(12 + -17x + -5x2) = 0
4 + 9x + 2x2 + (12 * -1 + -17x * -1 + -5x2 * -1) = 0
4 + 9x + 2x2 + (-12 + 17x + 5x2) = 0

Reorder the terms:
4 + -12 + 9x + 17x + 2x2 + 5x2 = 0

Combine like terms: 4 + -12 = -8
-8 + 9x + 17x + 2x2 + 5x2 = 0

Combine like terms: 9x + 17x = 26x
-8 + 26x + 2x2 + 5x2 = 0

Combine like terms: 2x2 + 5x2 = 7x2
-8 + 26x + 7x2 = 0

Solving
-8 + 26x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(2 + -7x) = 0

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857

Solution

x = {-4, 0.2857142857}

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