x(5x+10)=2x^2-3x+30

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Solution for x(5x+10)=2x^2-3x+30 equation:


Simplifying
x(5x + 10) = 2x2 + -3x + 30

Reorder the terms:
x(10 + 5x) = 2x2 + -3x + 30
(10 * x + 5x * x) = 2x2 + -3x + 30
(10x + 5x2) = 2x2 + -3x + 30

Reorder the terms:
10x + 5x2 = 30 + -3x + 2x2

Solving
10x + 5x2 = 30 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-30 + 10x + 3x + 5x2 + -2x2 = 30 + -3x + 2x2 + -30 + 3x + -2x2

Combine like terms: 10x + 3x = 13x
-30 + 13x + 5x2 + -2x2 = 30 + -3x + 2x2 + -30 + 3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-30 + 13x + 3x2 = 30 + -3x + 2x2 + -30 + 3x + -2x2

Reorder the terms:
-30 + 13x + 3x2 = 30 + -30 + -3x + 3x + 2x2 + -2x2

Combine like terms: 30 + -30 = 0
-30 + 13x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
-30 + 13x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-30 + 13x + 3x2 = 0 + 2x2 + -2x2
-30 + 13x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + 13x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -3x) = 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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-6, 1.666666667}

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