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Simplifying
36 + -19x = (5x + -3)(3x + -2)
Reorder the terms:
36 + -19x = (-3 + 5x)(3x + -2)
Reorder the terms:
36 + -19x = (-3 + 5x)(-2 + 3x)
Multiply (-3 + 5x) * (-2 + 3x)
36 + -19x = (-3(-2 + 3x) + 5x * (-2 + 3x))
36 + -19x = ((-2 * -3 + 3x * -3) + 5x * (-2 + 3x))
36 + -19x = ((6 + -9x) + 5x * (-2 + 3x))
36 + -19x = (6 + -9x + (-2 * 5x + 3x * 5x))
36 + -19x = (6 + -9x + (-10x + 15x2))
Combine like terms: -9x + -10x = -19x
36 + -19x = (6 + -19x + 15x2)
Add '19x' to each side of the equation.
36 + -19x + 19x = 6 + -19x + 19x + 15x2
Combine like terms: -19x + 19x = 0
36 + 0 = 6 + -19x + 19x + 15x2
36 = 6 + -19x + 19x + 15x2
Combine like terms: -19x + 19x = 0
36 = 6 + 0 + 15x2
36 = 6 + 15x2
Solving
36 = 6 + 15x2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-15x2' to each side of the equation.
36 + -15x2 = 6 + 15x2 + -15x2
Combine like terms: 15x2 + -15x2 = 0
36 + -15x2 = 6 + 0
36 + -15x2 = 6
Add '-36' to each side of the equation.
36 + -36 + -15x2 = 6 + -36
Combine like terms: 36 + -36 = 0
0 + -15x2 = 6 + -36
-15x2 = 6 + -36
Combine like terms: 6 + -36 = -30
-15x2 = -30
Divide each side by '-15'.
x2 = 2
Simplifying
x2 = 2
Take the square root of each side:
x = {-1.414213562, 1.414213562}
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