(4x+3)(x+4)=(3x+4)(x+7)

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Solution for (4x+3)(x+4)=(3x+4)(x+7) equation:


Simplifying
(4x + 3)(x + 4) = (3x + 4)(x + 7)

Reorder the terms:
(3 + 4x)(x + 4) = (3x + 4)(x + 7)

Reorder the terms:
(3 + 4x)(4 + x) = (3x + 4)(x + 7)

Multiply (3 + 4x) * (4 + x)
(3(4 + x) + 4x * (4 + x)) = (3x + 4)(x + 7)
((4 * 3 + x * 3) + 4x * (4 + x)) = (3x + 4)(x + 7)
((12 + 3x) + 4x * (4 + x)) = (3x + 4)(x + 7)
(12 + 3x + (4 * 4x + x * 4x)) = (3x + 4)(x + 7)
(12 + 3x + (16x + 4x2)) = (3x + 4)(x + 7)

Combine like terms: 3x + 16x = 19x
(12 + 19x + 4x2) = (3x + 4)(x + 7)

Reorder the terms:
12 + 19x + 4x2 = (4 + 3x)(x + 7)

Reorder the terms:
12 + 19x + 4x2 = (4 + 3x)(7 + x)

Multiply (4 + 3x) * (7 + x)
12 + 19x + 4x2 = (4(7 + x) + 3x * (7 + x))
12 + 19x + 4x2 = ((7 * 4 + x * 4) + 3x * (7 + x))
12 + 19x + 4x2 = ((28 + 4x) + 3x * (7 + x))
12 + 19x + 4x2 = (28 + 4x + (7 * 3x + x * 3x))
12 + 19x + 4x2 = (28 + 4x + (21x + 3x2))

Combine like terms: 4x + 21x = 25x
12 + 19x + 4x2 = (28 + 25x + 3x2)

Solving
12 + 19x + 4x2 = 28 + 25x + 3x2

Solving for variable 'x'.

Reorder the terms:
12 + -28 + 19x + -25x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 12 + -28 = -16
-16 + 19x + -25x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 19x + -25x = -6x
-16 + -6x + 4x2 + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-16 + -6x + 1x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Reorder the terms:
-16 + -6x + 1x2 = 28 + -28 + 25x + -25x + 3x2 + -3x2

Combine like terms: 28 + -28 = 0
-16 + -6x + 1x2 = 0 + 25x + -25x + 3x2 + -3x2
-16 + -6x + 1x2 = 25x + -25x + 3x2 + -3x2

Combine like terms: 25x + -25x = 0
-16 + -6x + 1x2 = 0 + 3x2 + -3x2
-16 + -6x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-16 + -6x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-2, 8}

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