(4x+7)(x-5)=16x+28

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Solution for (4x+7)(x-5)=16x+28 equation: 


Simplifying
(4x + 7)(x + -5) = 16x + 28

Reorder the terms:
(7 + 4x)(x + -5) = 16x + 28

Reorder the terms:
(7 + 4x)(-5 + x) = 16x + 28

Multiply (7 + 4x) * (-5 + x)
(7(-5 + x) + 4x * (-5 + x)) = 16x + 28
((-5 * 7 + x * 7) + 4x * (-5 + x)) = 16x + 28
((-35 + 7x) + 4x * (-5 + x)) = 16x + 28
(-35 + 7x + (-5 * 4x + x * 4x)) = 16x + 28
(-35 + 7x + (-20x + 4x2)) = 16x + 28

Combine like terms: 7x + -20x = -13x
(-35 + -13x + 4x2) = 16x + 28

Reorder the terms:
-35 + -13x + 4x2 = 28 + 16x

Solving
-35 + -13x + 4x2 = 28 + 16x

Solving for variable 'x'.

Reorder the terms:
-35 + -28 + -13x + -16x + 4x2 = 28 + 16x + -28 + -16x

Combine like terms: -35 + -28 = -63
-63 + -13x + -16x + 4x2 = 28 + 16x + -28 + -16x

Combine like terms: -13x + -16x = -29x
-63 + -29x + 4x2 = 28 + 16x + -28 + -16x

Reorder the terms:
-63 + -29x + 4x2 = 28 + -28 + 16x + -16x

Combine like terms: 28 + -28 = 0
-63 + -29x + 4x2 = 0 + 16x + -16x
-63 + -29x + 4x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-63 + -29x + 4x2 = 0

Factor a trinomial.
(-7 + -4x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1.75, 9}

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