6x^2=7x+5

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Solution for 6x^2=7x+5 equation:


Simplifying
6x2 = 7x + 5

Reorder the terms:
6x2 = 5 + 7x

Solving
6x2 = 5 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + -7x + 6x2 = 5 + 7x + -5 + -7x

Reorder the terms:
-5 + -7x + 6x2 = 5 + -5 + 7x + -7x

Combine like terms: 5 + -5 = 0
-5 + -7x + 6x2 = 0 + 7x + -7x
-5 + -7x + 6x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-5 + -7x + 6x2 = 0

Factor a trinomial.
(-1 + -2x)(5 + -3x) = 0

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

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 = {-0.5, 1.666666667}

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