12x^2=47x-40

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Solution for 12x^2=47x-40 equation:


Simplifying
12x2 = 47x + -40

Reorder the terms:
12x2 = -40 + 47x

Solving
12x2 = -40 + 47x

Solving for variable 'x'.

Reorder the terms:
40 + -47x + 12x2 = -40 + 47x + 40 + -47x

Reorder the terms:
40 + -47x + 12x2 = -40 + 40 + 47x + -47x

Combine like terms: -40 + 40 = 0
40 + -47x + 12x2 = 0 + 47x + -47x
40 + -47x + 12x2 = 47x + -47x

Combine like terms: 47x + -47x = 0
40 + -47x + 12x2 = 0

Factor a trinomial.
(5 + -4x)(8 + -3x) = 0

Subproblem 1

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Subproblem 2

Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667

Solution

x = {1.25, 2.666666667}

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