(5x+8)(x+2)=29x+28

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Solution for (5x+8)(x+2)=29x+28 equation:


Simplifying
(5x + 8)(x + 2) = 29x + 28

Reorder the terms:
(8 + 5x)(x + 2) = 29x + 28

Reorder the terms:
(8 + 5x)(2 + x) = 29x + 28

Multiply (8 + 5x) * (2 + x)
(8(2 + x) + 5x * (2 + x)) = 29x + 28
((2 * 8 + x * 8) + 5x * (2 + x)) = 29x + 28
((16 + 8x) + 5x * (2 + x)) = 29x + 28
(16 + 8x + (2 * 5x + x * 5x)) = 29x + 28
(16 + 8x + (10x + 5x2)) = 29x + 28

Combine like terms: 8x + 10x = 18x
(16 + 18x + 5x2) = 29x + 28

Reorder the terms:
16 + 18x + 5x2 = 28 + 29x

Solving
16 + 18x + 5x2 = 28 + 29x

Solving for variable 'x'.

Reorder the terms:
16 + -28 + 18x + -29x + 5x2 = 28 + 29x + -28 + -29x

Combine like terms: 16 + -28 = -12
-12 + 18x + -29x + 5x2 = 28 + 29x + -28 + -29x

Combine like terms: 18x + -29x = -11x
-12 + -11x + 5x2 = 28 + 29x + -28 + -29x

Reorder the terms:
-12 + -11x + 5x2 = 28 + -28 + 29x + -29x

Combine like terms: 28 + -28 = 0
-12 + -11x + 5x2 = 0 + 29x + -29x
-12 + -11x + 5x2 = 29x + -29x

Combine like terms: 29x + -29x = 0
-12 + -11x + 5x2 = 0

Factor a trinomial.
(-4 + -5x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 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 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-0.8, 3}

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