(3x-2)(x+1)=18x+4

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Solution for (3x-2)(x+1)=18x+4 equation:


Simplifying
(3x + -2)(x + 1) = 18x + 4

Reorder the terms:
(-2 + 3x)(x + 1) = 18x + 4

Reorder the terms:
(-2 + 3x)(1 + x) = 18x + 4

Multiply (-2 + 3x) * (1 + x)
(-2(1 + x) + 3x * (1 + x)) = 18x + 4
((1 * -2 + x * -2) + 3x * (1 + x)) = 18x + 4
((-2 + -2x) + 3x * (1 + x)) = 18x + 4
(-2 + -2x + (1 * 3x + x * 3x)) = 18x + 4
(-2 + -2x + (3x + 3x2)) = 18x + 4

Combine like terms: -2x + 3x = 1x
(-2 + 1x + 3x2) = 18x + 4

Reorder the terms:
-2 + 1x + 3x2 = 4 + 18x

Solving
-2 + 1x + 3x2 = 4 + 18x

Solving for variable 'x'.

Reorder the terms:
-2 + -4 + 1x + -18x + 3x2 = 4 + 18x + -4 + -18x

Combine like terms: -2 + -4 = -6
-6 + 1x + -18x + 3x2 = 4 + 18x + -4 + -18x

Combine like terms: 1x + -18x = -17x
-6 + -17x + 3x2 = 4 + 18x + -4 + -18x

Reorder the terms:
-6 + -17x + 3x2 = 4 + -4 + 18x + -18x

Combine like terms: 4 + -4 = 0
-6 + -17x + 3x2 = 0 + 18x + -18x
-6 + -17x + 3x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-6 + -17x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

Subproblem 2

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

Solution

x = {-0.3333333333, 6}

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