x(8x+7)=3x^2-19x+24

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Solution for x(8x+7)=3x^2-19x+24 equation:


Simplifying
x(8x + 7) = 3x2 + -19x + 24

Reorder the terms:
x(7 + 8x) = 3x2 + -19x + 24
(7 * x + 8x * x) = 3x2 + -19x + 24
(7x + 8x2) = 3x2 + -19x + 24

Reorder the terms:
7x + 8x2 = 24 + -19x + 3x2

Solving
7x + 8x2 = 24 + -19x + 3x2

Solving for variable 'x'.

Reorder the terms:
-24 + 7x + 19x + 8x2 + -3x2 = 24 + -19x + 3x2 + -24 + 19x + -3x2

Combine like terms: 7x + 19x = 26x
-24 + 26x + 8x2 + -3x2 = 24 + -19x + 3x2 + -24 + 19x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-24 + 26x + 5x2 = 24 + -19x + 3x2 + -24 + 19x + -3x2

Reorder the terms:
-24 + 26x + 5x2 = 24 + -24 + -19x + 19x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
-24 + 26x + 5x2 = 0 + -19x + 19x + 3x2 + -3x2
-24 + 26x + 5x2 = -19x + 19x + 3x2 + -3x2

Combine like terms: -19x + 19x = 0
-24 + 26x + 5x2 = 0 + 3x2 + -3x2
-24 + 26x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-24 + 26x + 5x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -5x) = 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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Solution

x = {-6, 0.8}

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