6x^2=20-7x

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Solution for 6x^2=20-7x equation:


Simplifying
6x2 = 20 + -7x

Solving
6x2 = 20 + -7x

Solving for variable 'x'.

Reorder the terms:
-20 + 7x + 6x2 = 20 + -7x + -20 + 7x

Reorder the terms:
-20 + 7x + 6x2 = 20 + -20 + -7x + 7x

Combine like terms: 20 + -20 = 0
-20 + 7x + 6x2 = 0 + -7x + 7x
-20 + 7x + 6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-20 + 7x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(4 + -3x) = 0

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {-2.5, 1.333333333}

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