(x-1)(x+3)=4x+45

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Solution for (x-1)(x+3)=4x+45 equation:


Simplifying
(x + -1)(x + 3) = 4x + 45

Reorder the terms:
(-1 + x)(x + 3) = 4x + 45

Reorder the terms:
(-1 + x)(3 + x) = 4x + 45

Multiply (-1 + x) * (3 + x)
(-1(3 + x) + x(3 + x)) = 4x + 45
((3 * -1 + x * -1) + x(3 + x)) = 4x + 45
((-3 + -1x) + x(3 + x)) = 4x + 45
(-3 + -1x + (3 * x + x * x)) = 4x + 45
(-3 + -1x + (3x + x2)) = 4x + 45

Combine like terms: -1x + 3x = 2x
(-3 + 2x + x2) = 4x + 45

Reorder the terms:
-3 + 2x + x2 = 45 + 4x

Solving
-3 + 2x + x2 = 45 + 4x

Solving for variable 'x'.

Reorder the terms:
-3 + -45 + 2x + -4x + x2 = 45 + 4x + -45 + -4x

Combine like terms: -3 + -45 = -48
-48 + 2x + -4x + x2 = 45 + 4x + -45 + -4x

Combine like terms: 2x + -4x = -2x
-48 + -2x + x2 = 45 + 4x + -45 + -4x

Reorder the terms:
-48 + -2x + x2 = 45 + -45 + 4x + -4x

Combine like terms: 45 + -45 = 0
-48 + -2x + x2 = 0 + 4x + -4x
-48 + -2x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-6, 8}

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