(4x+7)(x-3)=16x+28

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Solution for (4x+7)(x-3)=16x+28 equation:


Simplifying
(4x + 7)(x + -3) = 16x + 28

Reorder the terms:
(7 + 4x)(x + -3) = 16x + 28

Reorder the terms:
(7 + 4x)(-3 + x) = 16x + 28

Multiply (7 + 4x) * (-3 + x)
(7(-3 + x) + 4x * (-3 + x)) = 16x + 28
((-3 * 7 + x * 7) + 4x * (-3 + x)) = 16x + 28
((-21 + 7x) + 4x * (-3 + x)) = 16x + 28
(-21 + 7x + (-3 * 4x + x * 4x)) = 16x + 28
(-21 + 7x + (-12x + 4x2)) = 16x + 28

Combine like terms: 7x + -12x = -5x
(-21 + -5x + 4x2) = 16x + 28

Reorder the terms:
-21 + -5x + 4x2 = 28 + 16x

Solving
-21 + -5x + 4x2 = 28 + 16x

Solving for variable 'x'.

Reorder the terms:
-21 + -28 + -5x + -16x + 4x2 = 28 + 16x + -28 + -16x

Combine like terms: -21 + -28 = -49
-49 + -5x + -16x + 4x2 = 28 + 16x + -28 + -16x

Combine like terms: -5x + -16x = -21x
-49 + -21x + 4x2 = 28 + 16x + -28 + -16x

Reorder the terms:
-49 + -21x + 4x2 = 28 + -28 + 16x + -16x

Combine like terms: 28 + -28 = 0
-49 + -21x + 4x2 = 0 + 16x + -16x
-49 + -21x + 4x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-49 + -21x + 4x2 = 0

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

Subproblem 1

Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 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 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-1.75, 7}

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