(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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