(2x+5)(x-4)=15

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Solution for (2x+5)(x-4)=15 equation: 


Simplifying
(2x + 5)(x + -4) = 15

Reorder the terms:
(5 + 2x)(x + -4) = 15

Reorder the terms:
(5 + 2x)(-4 + x) = 15

Multiply (5 + 2x) * (-4 + x)
(5(-4 + x) + 2x * (-4 + x)) = 15
((-4 * 5 + x * 5) + 2x * (-4 + x)) = 15
((-20 + 5x) + 2x * (-4 + x)) = 15
(-20 + 5x + (-4 * 2x + x * 2x)) = 15
(-20 + 5x + (-8x + 2x2)) = 15

Combine like terms: 5x + -8x = -3x
(-20 + -3x + 2x2) = 15

Solving
-20 + -3x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-20 + -15 + -3x + 2x2 = 15 + -15

Combine like terms: -20 + -15 = -35
-35 + -3x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-35 + -3x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3.5, 5}

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