(4x-3)(x+7)=38x-9

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Solution for (4x-3)(x+7)=38x-9 equation: 


Simplifying
(4x + -3)(x + 7) = 38x + -9

Reorder the terms:
(-3 + 4x)(x + 7) = 38x + -9

Reorder the terms:
(-3 + 4x)(7 + x) = 38x + -9

Multiply (-3 + 4x) * (7 + x)
(-3(7 + x) + 4x * (7 + x)) = 38x + -9
((7 * -3 + x * -3) + 4x * (7 + x)) = 38x + -9
((-21 + -3x) + 4x * (7 + x)) = 38x + -9
(-21 + -3x + (7 * 4x + x * 4x)) = 38x + -9
(-21 + -3x + (28x + 4x2)) = 38x + -9

Combine like terms: -3x + 28x = 25x
(-21 + 25x + 4x2) = 38x + -9

Reorder the terms:
-21 + 25x + 4x2 = -9 + 38x

Solving
-21 + 25x + 4x2 = -9 + 38x

Solving for variable 'x'.

Reorder the terms:
-21 + 9 + 25x + -38x + 4x2 = -9 + 38x + 9 + -38x

Combine like terms: -21 + 9 = -12
-12 + 25x + -38x + 4x2 = -9 + 38x + 9 + -38x

Combine like terms: 25x + -38x = -13x
-12 + -13x + 4x2 = -9 + 38x + 9 + -38x

Reorder the terms:
-12 + -13x + 4x2 = -9 + 9 + 38x + -38x

Combine like terms: -9 + 9 = 0
-12 + -13x + 4x2 = 0 + 38x + -38x
-12 + -13x + 4x2 = 38x + -38x

Combine like terms: 38x + -38x = 0
-12 + -13x + 4x2 = 0

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


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
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
Solution
x = {-0.75, 4}

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