(4x+5)(x-4)=12x+15

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Solution for (4x+5)(x-4)=12x+15 equation: 


Simplifying
(4x + 5)(x + -4) = 12x + 15

Reorder the terms:
(5 + 4x)(x + -4) = 12x + 15

Reorder the terms:
(5 + 4x)(-4 + x) = 12x + 15

Multiply (5 + 4x) * (-4 + x)
(5(-4 + x) + 4x * (-4 + x)) = 12x + 15
((-4 * 5 + x * 5) + 4x * (-4 + x)) = 12x + 15
((-20 + 5x) + 4x * (-4 + x)) = 12x + 15
(-20 + 5x + (-4 * 4x + x * 4x)) = 12x + 15
(-20 + 5x + (-16x + 4x2)) = 12x + 15

Combine like terms: 5x + -16x = -11x
(-20 + -11x + 4x2) = 12x + 15

Reorder the terms:
-20 + -11x + 4x2 = 15 + 12x

Solving
-20 + -11x + 4x2 = 15 + 12x

Solving for variable 'x'.

Reorder the terms:
-20 + -15 + -11x + -12x + 4x2 = 15 + 12x + -15 + -12x

Combine like terms: -20 + -15 = -35
-35 + -11x + -12x + 4x2 = 15 + 12x + -15 + -12x

Combine like terms: -11x + -12x = -23x
-35 + -23x + 4x2 = 15 + 12x + -15 + -12x

Reorder the terms:
-35 + -23x + 4x2 = 15 + -15 + 12x + -12x

Combine like terms: 15 + -15 = 0
-35 + -23x + 4x2 = 0 + 12x + -12x
-35 + -23x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-35 + -23x + 4x2 = 0

Factor a trinomial.
(-5 + -4x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

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 = {-1.25, 7}

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