# 2x(4x-7)+3=(2x-7)(3x+4)+2x^2

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## Solution for 2x(4x-7)+3=(2x-7)(3x+4)+2x^2 equation:

Simplifying
2x(4x + -7) + 3 = (2x + -7)(3x + 4) + 2x2

Reorder the terms:
2x(-7 + 4x) + 3 = (2x + -7)(3x + 4) + 2x2
(-7 * 2x + 4x * 2x) + 3 = (2x + -7)(3x + 4) + 2x2
(-14x + 8x2) + 3 = (2x + -7)(3x + 4) + 2x2

Reorder the terms:
3 + -14x + 8x2 = (2x + -7)(3x + 4) + 2x2

Reorder the terms:
3 + -14x + 8x2 = (-7 + 2x)(3x + 4) + 2x2

Reorder the terms:
3 + -14x + 8x2 = (-7 + 2x)(4 + 3x) + 2x2

Multiply (-7 + 2x) * (4 + 3x)
3 + -14x + 8x2 = (-7(4 + 3x) + 2x * (4 + 3x)) + 2x2
3 + -14x + 8x2 = ((4 * -7 + 3x * -7) + 2x * (4 + 3x)) + 2x2
3 + -14x + 8x2 = ((-28 + -21x) + 2x * (4 + 3x)) + 2x2
3 + -14x + 8x2 = (-28 + -21x + (4 * 2x + 3x * 2x)) + 2x2
3 + -14x + 8x2 = (-28 + -21x + (8x + 6x2)) + 2x2

Combine like terms: -21x + 8x = -13x
3 + -14x + 8x2 = (-28 + -13x + 6x2) + 2x2

Combine like terms: 6x2 + 2x2 = 8x2
3 + -14x + 8x2 = -28 + -13x + 8x2

Add '-8x2' to each side of the equation.
3 + -14x + 8x2 + -8x2 = -28 + -13x + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
3 + -14x + 0 = -28 + -13x + 8x2 + -8x2
3 + -14x = -28 + -13x + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
3 + -14x = -28 + -13x + 0
3 + -14x = -28 + -13x

Solving
3 + -14x = -28 + -13x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13x' to each side of the equation.
3 + -14x + 13x = -28 + -13x + 13x

Combine like terms: -14x + 13x = -1x
3 + -1x = -28 + -13x + 13x

Combine like terms: -13x + 13x = 0
3 + -1x = -28 + 0
3 + -1x = -28

Add '-3' to each side of the equation.
3 + -3 + -1x = -28 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = -28 + -3
-1x = -28 + -3

Combine like terms: -28 + -3 = -31
-1x = -31

Divide each side by '-1'.
x = 31

Simplifying
x = 31`