(x+3)(4x-5)=15

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Solution for (x+3)(4x-5)=15 equation: 


Simplifying
(x + 3)(4x + -5) = 15

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

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

Multiply (3 + x) * (-5 + 4x)
(3(-5 + 4x) + x(-5 + 4x)) = 15
((-5 * 3 + 4x * 3) + x(-5 + 4x)) = 15
((-15 + 12x) + x(-5 + 4x)) = 15
(-15 + 12x + (-5 * x + 4x * x)) = 15
(-15 + 12x + (-5x + 4x2)) = 15

Combine like terms: 12x + -5x = 7x
(-15 + 7x + 4x2) = 15

Solving
-15 + 7x + 4x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -15 + 7x + 4x2 = 15 + -15

Combine like terms: -15 + -15 = -30
-30 + 7x + 4x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-30 + 7x + 4x2 = 0

Factor a trinomial.
(-15 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -4x)' equal to zero and attempt to solve:

Simplifying
-15 + -4x = 0

Solving
-15 + -4x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4x = 0 + 15
-4x = 0 + 15

Combine like terms: 0 + 15 = 15
-4x = 15

Divide each side by '-4'.
x = -3.75

Simplifying
x = -3.75

Subproblem 2
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
Solution
x = {-3.75, 2}

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